
SBBB&ftS 



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WORKS OF PROF. A. P. JAMISON 



PUBLISHED BY 



JOHN WILEY & SONS. 



Elements of Mechanical Drawing. 

Their Application and A Course in Mechanical 
Drawing for Engineering Students. 8vo, xii-f- 
226 pages, including 57 full-page plates and 82 fig- 
ures in the text. Cloth, $2.50. 

Advanced Mechanical Drawing. 

A Text for Engineering Students. 8vo, ix + 177 
pages, including 27 full-page plates and 117 figures 
in the text. Cloth, $2.00. 



ELEMENTS OF 

MECHANICAL DRAWING 

THEIR APPLICATION AND 

A COURSE IN MECHANICAL DRAWING 
FOR ENGINEERING STUDENTS. 



BY 



ALPHA PIERCE JAMISON, M.E., 

Assistant Professor of Mechanical Drawing in Purdu4. 



SECOND EDITION, REVISED. 
FIFTH THOUSAND. 



NEW YORK: 
JOHN WILEY & SONS. 

London: CHAPMAN & HALL, Limited, 

191 1 






Copyright, 1904* 



BY 



A. P. JAMISON. 



By Transfer 

NOV 1 6 '^20 



• . . 



THE SCIENTIFIC PRESS 

ROBERT ORUMMONO ANO COMPANY 

BROOKLYN, N. Y. 

\ 






PREFACE. 



Having in charge the instruction of the Freshman Class, 
Purdue University, in the subject, the writer has compiled the 
accompanying notes on Mechanical Drawing to facilitate the 
work of administration. 

The intent, throughout, has been to prepare a work embracing 
those branches of the subject necessary to give the student such 
knowledge as will prepare him to pursue a course in Engineering, 
and such practice in drawing as will qualify him to do ordinary 
commercial draughting. 

The work is arranged for students having a knowledge of 
plane geometry such as is offered in the High Schools, Prepara- 
tory Schools, and Colleges. 

Acknowledgment is made of many valuable suggestions and 
criticisms offered by Professors M. J. and Katherine E. Golden, 
and by Messrs. R. B. Trueblood and A. M. Wilson, co-laborers 
in the work of administration. 

A. P. Jamison. 

Lafayette, Ind., March, 1904. 



111 



CONTENTS. 

PART I. 

CHAPTER I. 

Elementary Principles and Definitions, 
section page 

i. Drawing I 

2. Drawing of Objects as they Appear I 

3. Drawing of Objects as they Exist I 

4. Detail Drawing o 

5. Assembled Drawing * 

6. The Divisions of Drawing o 

7. Shop Drawing 3 

8. Show Drawing 3 

9. Relation of the Lines of an Object 3 

10. Relation of the Faces of an Object 4 

11. Choosing the Front Face 5 

12. Relation of Lines and Faces Shown by a Complete Mechanical Drawing 

of a Cube 5 

13. Arrangement of the Drawing 6 

14. Definition of Mechanical Drawing 6 

15. Naming the Faces of an Object 6 

16. Elevations 8 

17. Plan and Bottom 8 

18. Sections 8 

19. Longitudinal Section 8 

20. Transverse Section 8 

21. Angular Section 9 

22. Full Section 9 

23. Half Section 9 

24. Detail Section 9 

25. Explanatory of Sections 9 

26. Drawing Sections II 

27. Arrangement of Sections on the Drawing 11 

28. Cross-hatching II 

V 



vi CONTENTS. 

SECTION PAGE 

29. Lines •••••••••••••••••••• 12 

30. Lines of the Drawing 12 

31. Border Lines 12 

32. Center Lines „ 12 

2,2,. Section Lines , 13 

34. Construction Lines 14 

35. Projection Lines 14 

36. Dimension Lines 14 

37. Guide Lines 14 

38. Light and Shade 14 

39. Line Shading 14 

40. Shade or Shadow Lining 14 

41. Drawing to Scale 16 

42. Choosing the Scale 16 

43 Balance and Symmetry of a Drawing 18 

44. Flexibility of the Drawing. . 19 

45. Dimensioning 20 

46. Selection of the Necessary Views 21 

47. Usual Number of Views. , 22 

48. Use of Dashed and Dotted Lines to Reduce the Number of Views • 22 

49. Beginning to Draw 22 

50. Drafting-room Practice 23 

51. The Time Element in Drawing 24 

52. Conventions ••• 25 

CHAPTER II. 

Letters, Figures, and Lettering. 

53. Fundamentals 26 

54. A Study of Letters „ 28 

55. Modifications 32 

56. Suggestions 34 

57. Combinations and Spacings 34 

58. Figures 1 34 

59. Fractions 36 

60. Lower-case Alphabet. 36 

61. Mechanical Letters, 37 

CHAPTER m. 

Projection. 

62. Scenographic Projection ••••••••••• 39 

63. Orthographic Projection •••••••••• 39 

64. The Planes of Projection 40 

65. The Four Quadrants 40 



CONTENTS. vii 

SECTION PAGE 

66. The Projection of a Point, with the Planes V and H at Right Angles 42 

67. The Planes V and H Revolved t 43 

68. The Conventional Projection of a Point 43 

69. The Conventional Assumption of a Point „ 44 

70. The Projection of Any Straight Line 45 

71. The Projection of a Line which is Parallel to one of the Planes of Pro- 

jection c c „ , 42 

72. To Find the True Length of a Line r „ e . „ 46 

73. The Projection of a Straight Line which is Perpendicular to One of the 

Planes of Projection 48 

74. The Assumption of a Plane 48 

75. To Draw the Projections of a Hollow Cube 49 

76. To Draw the Projections of a Hexagonal Nut 51 

77. The Projections of a Small Hand-wheel 54 

78. Projections of the Frustum of a Pyramid 57 

79. Projections of the Frustum of a Cone 62 

80. The Intersection of Two Cylinders at Right Angles 63 

81. The Intersection of a Cone and Cylinder 67 

82. The Intersection of Two Cylinders at an Angle of 45 . 70 

83. A Practical Development 71 

84. First and Third Quadrant Projections . . . . 73 

85. Isometric Projection 74 

To Dimension an Isometric Drawing 78 

Isometric Scales 78 

86. Elementary Examples ••••••••••• 80 



CHAPTER IV. 

Drawing Tools and Materials. 

87. Introductory , S^ 

88. The Ruling-pen 85 

89. The Compass 91 

90. The Dividers 93 

91. The Bow-pen 94 

92. The Bow-pencil 95 

93. The Bow-dividers 96 

94. The Box fcr Leads 96 

95. The Care of Instruments 96 

96. Drawing-boards 96 

97. The T-Square 97 

98. The Triangles 98 

99. Irregular Curves 100 

100. The Architect's Scale 100 

101. Thumb-tacks * .... 103 



viii CONTENTS. 

SECTION PAGE 

102. Pencils and Leads •••••/••• „ 104 

103. Pens and Pen-holders 106 

104. Erasers. . . 107 

105. Ink » 107 

106. Rag and Blotter. 108 

107. Horn Centers 108 

108. Section Liners. 108 

109. Erasing-shields 109 

1 10. Protractors 109 

in. Scale-guard 109 

112. Proportional Dividers 109 

113. Erasing-knives 109 

1 14. Soap-stone Pencil 109 

1 15. Paper 109 

116. To Make an Erasure on Paper in 

117. Profile and Cross-section Paper 112 

118. Tracing-paper 112 

119. Blue-print Paper 112 

120. Tracing-cloth 113 

121. To Make an Erasure on Tracing-cloth 113 



CHAPTER V. 

The Reproduction of Drawings. 

122. Introductory 115 

123. Blue-printing 116 

124. Exposure 117 

125. Washing 118 

126. Drying 118 

127. Photography 119 

128. The Hectograph 119 

129. The Mimeograph 119 



CHAPTER VI. 
Patent-office Drawings. 

130. Introductory 120 

131. Drawings 120 

132. Requisites of Drawings 120 

133 Three Editions of Drawings 120 

134. Uniform Standard 121 

135. Paper and Ink 121 



CONTENTS. ix 

SECTION - PAGB 

136. Size of Sheet and Marginal Lines 121 

137. Character and Color of Lines 121 

138. Few Lines and Little or no Shading 121 

139. Scale of the Drawing 122 

140. Letters of Reference 122 

141. Signatures of Inventor and Witnesses 124 

142. Title 124 

143. Large Views 124 

144. Figures for Gazette 124 

145. Drawings to be Rolled for Transmission 124 

146. No Stamp, Advertisement, or Address Permitted on the Face of Draw- 

ings 124 

147. Drawings for Designs * 125 

148. Drawings for Reissue Applications 125 

149. Defective Drawings 125 

150. Drawings Furnished by Office •••••••••• 125 



CHAPTER VIL 
Gearing. 

151. Introductory 126 

152. Fundamental Curves 126 

The Cycloid 126 

The Epicycloid 127 

The Hypocycloid 128 

The Involute 129 

J53. Glossary of Terms 129 

Tooth 129 

Space , 129 

Circular Pitch 129 

Tooth Face 130 

Tooth Flank 130 

Front of the Tooth 130 

Back of the Tooth 130 

Pitch Point , 130 

Addendum Circle 130 

Root Circle 130 

Clearance 130 

Dedendum Circle 130 

Depth of Tooth 130 

Fillet 130 

Pitch Diameter 130 

Diametral Pitch- 130 

Driver 130 

Follower 130 



x CONTENTS. 

SECTION PAGB 

154. Usual Proportions for Teeth 130 

155. Development of Formulae 131 

156. Kinds of Gears 131 

Spur-gears 132 

Rack 232 

Annual or Internal Gear. 132 

157. Systems of Teeth 132 

Cycloidal !32 

Involute 132 

158. Interchangeability 132 

159. Methods of Drawing the Tooth Outline 132 

Exact Method 133 

Approximate Method 133 

160. Spur-gears 133 

Exact, Non -interchangeable, Cycloidal 133 

Exact, Interchangeable, Cycloidal 134 

Exact Involute 135 

Approximate Cycloidal 136 

Approximate Involute 138 

161. Rack and Pinion 138 

Exact, Non -interchangeable, Cycloidal 138 

Exact, Interchangeable, Cycloidal 141 

Exact Involute 141 

Approximate Cycloidal 141 

Approximate Involute 142 

162. Internal Gears 142 

Exact Cycloidal • 142 

Exact Involute 144 

Approximate Cycloidal 144 

Approximate Involute 144 



CHAPTER VIIL 
Color Work. 

tinting. 

163. Introductory. 145 

164. Outfit 145 

165. Making a Stretch 146 

166. Mixing the Colors 146 

167. Flat Wash * 147 

168. Shading 147 

STIPPLING. 

169. Introductory 149 

170. Method of Procedure 150 



CONTENTS. 



XI 



PART II. 



CHAPTER IX. 
Sketching. 



SBCTION 

171 

172 



PAGB 



173- 
174. 

175. 
I76. 

177. 
178. 
179. 
I80. 
I8l. 
l82. 
183. 
184. 
185. 
186. 
187. 
188. 
189. 
I90. 
191. 



Introductory. 152 

Sheet No, 1 152 

2 152 

3 154 

4 154 

5 • 155 

6 to 20 inclusive 155 



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157 
170 

170 
170 
170 
170 
170 
170 
170 
170 
171 



34 to 40 inclusive 171 



CHAPTER X. 



The Mechanical Execution of Drawings. 

192. Introductory 172 

193. Sheet No. 1 172 

176 

176 

178 

178 

182 

184 

o... 188 

188 

190 

192 

192 



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CONTENTS. 



SECTION PAGI 

205. Sheet No. 13 196 



206. 
207. 
208. 
209. 
210. 
211. 
212. 
213. 
214. 
215. 
216. 
217. 
218. 
219. 
220. 
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19. 
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23- 
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25. 
26. 

27. 

28. 

29. 

3°. 
3i. 



196 
19& 

200 
200- 
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20a 
20S 
208- 

2C8 

21a 
210 
210 
210 
210 
216 

218 

220 

222c 



32 to 36 inclusive •• •#••••••••*• 225 



TABLEa 

225. Explanatory •••••••••••••• 225 

Steam- and Gas-pipe 225 

Bolts and Nuts 226 

Gear Teeth 137, 138 



MECHANICAL DRAWING. 



PART I. 



CHAPTER I. 

ELEMENTARY PRINCIPLES AND DEFINITIONS. 

1. Drawing. — Drawing is the art of putting one's impressions 
into visible form, and may be divided into two general classes: 
(i) the drawing of objects viewed from a finite distance, and 
(2) the drawing of objects viewed from an infinite distance. 

2. Drawing of Objects as they Appear. — By the first class 
of drawing is meant the free-hand work of the artist, drawings 
of things as they appear to the eye, as they impress one. In 
such drawing there is but one point of sight * — the observer's 
eye — and the lines of sight f are straight lines radiating from 
this one point and extending to the different points of the object 
or objects, as the case may be. (See Fig. 1.) Paintings of 
landscapes, portraits, miniatures, the sketch-work of the news- 
paper artist, etc., are examples of this class of drawing. 

3. Drawing of Objects as they Exist. — By the second class 
of drawing is meant the drawing of objects as they actually exist 
and not as they appear to the eye. Such drawing is called 
"Mechanical Drawing," and the point of sight being at an infinite 
distance, the lines of sight are practically parallel and are so 

* The point of sight is that point, imaginary or real, from which an object is 
viewed; we see with two eyes, but only one point of sight is assumed. 

f A line of sight is an imaginary straight line connecting any point of the object 
and the point of sight. 



MECHANICAL DRAWING. 



assumed. Fig. 2 depicts the lines of sight for such drawing. 
Drawings of machinery, bridges, masonry construction, plans for 



Lines 




DRAWING ^T 



SHOWING THE POINT OF 



5IGHT AT A FINITE DISTANCE X V% 



buildings, etc., are examples of this class of drawing, and this is 
the kind of drawing with which engineers are concerned. 




DRAWING K^ 

SHOWING THE POI 



OF SIGHT AT AN 
INFINITE DISTANCE 



Fig. 2 



Mechanical Drawing may, in turn, be divided into two 
general classes: (1) detail drawing and (2) assembled drawing. 



ELEMENTARY PRINCIPLES AND DEFINITIONS. 



4. Detail Drawing. — To detail means to separate, to "tell" 
in detail; detail drawing means to separate an object — a machine, 
for example — into its various parts and to tell of each by a mechani- 
cal drawing of it. Detail drawings are used for shop purposes, 
that is, for "getting out ' the piece — for its manufacture, 

5. Assembled Drawing. — To assemble means to collect into 
one place or body; assembled drawing means to collect the vari- 
ous parts of an object — a machine, again, for example — and to 
draw it assembled as a whole. Assembled drawings are to 
"picture" the object as it will appear when complete. Such 
drawings are mostly used for erection purposes. 

Detail and assembled drawing may be subdivided into two 
other general classes: (1) shop drawing and (2) show drawing, 
presenting the subject "Drawing" thus: 

6. The Divisions of Drawing. 

Drawing of objects as they appear, called Per- 
spective Drawing. 

(The point of sight at a finite distance.) 



Drawing. 



Mechanical Drawing. 

(The point of sight at an ' 
infinite distance.) 



Detail ( Shop drawing. 
Drawing. ( Show drawing. 

Assembled ( Shop drawing. 
Drawing. ( Show drawing. 

7. Shop Drawing. — A shop drawing is a drawing to facilitate 
manufacture, and may be a detail or an assembled drawing, or 
both. It is usually an outline * drawing, very plain and free 
from ornamentation. 

8. Show Drawing. — A show drawing is a drawing calculated 
to facilitate the sale of an article. It is usually an ornamented 
drawing,f and is used for catalogue and "show" purposes. 

9. Relation of the Lines of an Object. — Every line of an 
object bears a certain relation to every other line of the same 
object, and in a mechanical drawing of that object the lines of 

* An outline drawing is a single -line drawing of the outline of an object. 
f An ornamented drawing is a drawing beautified by the addition of shades 
and shadows, colors, ornamental lettering, etc 



MECHANICAL DRAWING. 



the drawing must be so arranged as to present this relation to 
the eye. 

For example, consider a cube: all of its edges are straight 
lines, and are either parallel or perpendicular to one another; 
therefore, in the mechanical drawing of the cube all of the lines 
of the drawing must be straight lines either parallel or perpen- 
dicular to one another; furthermore, two adjacent edges of the 
same face are at right angles to each other, and opposite edges 
are parallel; hence in the me hanical drawing of that face the 
two adjacent lines must form a right angle and opposite lines 
must be parallel. From this it is obvious that the mechanical 
drawing of any one face of a cube is a perfect square. 

10. Relation of the Faces of an Object. — To maintain the 
relation of the lines of an object it is necessary that a separate 




Fig. 3. 
A Perspective Drawing. 

drawing of every face, or side, be constructed, for, in addition 
to the relation of the lines of an object, the faces of that object 
bear a definite relation to one another. To depict the relation 
of the faces of an object they are referred to one face called 
the " front face." 



ELEMENTARY PRINCIPLES AND DEFINITIONS. 5 

ii. Choosing the Front Face.— To represent these relations 
on paper it is necessary that the front face be decided on. In 
most cases this is readily determined by the objects' use and 
natural position. 

For example, consider the ordinary dwelling-house: it fronts 
a certain way and has a well-understood front. Facing this end 
of the building, one views the front face. (Fig. 3.) That face 
on the right hand is called the right face or side; that on the left, 
the left face or side; the face at the rear, the rear face; etc. 

This reasoning applies to any object as well as to the building 
in question; but should there be no well-defined front face, the 
choosing of one is optional with the draughtsman. 

12. Relation of Lines and Faces Shown by a Complete 
Mechanical Drawing of a Cube. — Having determined upon the 
front face of an object, construct a drawing representing all the 
lines of that face in their true position and relation with respect 
to one another. For a cube, as before stated, the drawing of 
the front face will be a perfect square; likewise, the drawing of all 
of the faces will be perfect squares. Now to "show" the relation 
of these various faces : — 



F E A 


Top 


B F 


Rear 


Lt.Side 


Front 


Rt.Side 


G I 


H D 

Fig. 4. 


Bottom 


c G 



H G 

A Mechanical Drawing. 



6 MECHANICAL DRAWING. 

(Fig. 4.) Beginning with the front face, A-B-C-D, drawn, the 
right face is at the right side of the front face and is tangent to 
it, having the line (edge) B-C in common with it; the left face is 
at the left of the front face and has the line (edge) A-D in com- 
mon with it; the bottom is at the bottom and is tangent along 
the line D-C\ the top face is at the top and has the line (edge) 
A-B in common with the front face. 

The rear face yet remains to be provided for: this face has 
an edge in common with the right face, one with the left face, 
one with the top and one with the bottom face. The drawing 
representing the rear face may be placed tangent to any one of 
the drawings representing the above faces; the one taken is 
usually determined by the limits of the paper, but is optional 
with the draughtsman. 

13. Arrangement of the Drawing. — Should all drawings be 
constructed with adjacent sides tangent along common lines the 
drawings would not admit of the convenient addition of dimen- 
sion lines, figures, and notes — details necessary to every drawing; 
also, such an arrangement would only apply to rectangular 
figures. For the convenient application of the foregoing principles 
the drawings are separated an optional distance (Fig. 1, Plate 
No. 1), those at the sides of the front face — the right and left 
faces — being moved in a horizontal direction only, and those 
at the top and bottom moved in a vertical direction only. 

It will be observed that all of the drawings are contained 
between two pairs of lines, one pair horizontal and the other 
vertical; should one or more of the drawings be "out of line" 
with these two pairs of lines the drawing would be incorrect. 

14. Definition of Mechanical Drawing. — From the fore- 
going, a mechanical drawing of an object may be said to be a 
separate drawing of each face of the object, and these several 
drawings so arranged as to bear the proper relation to one 
another. 

15. Naming the Drawings. — In the explanation mention has 
been made of the different faces of an object; the several 
drawings representing these faces are now to be named. 



ELEMENTARY PRINCIPLES AND DEFINITIONS. 



PLATE No. i. 



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8 MECHANICAL DRAWING. 

The drawing representing the front face of an object is called 
a front view or front elevation, and drawings of the right and 
left faces are called side views, right and left elevations respect- 
ively, or collectively side elevations, and the drawing representing 
the rear face is called the rear view or rear elevation. 

16. Elevations. — Elevations are views in which all of tlie 
lines of sight are parallel, horizontal lines. Side elevations are 
at right angles to the front and rear elevations, and vice versa. 
Elevations should always be between the same limiting pair of 
horizontal lines. (Fig. i, Plate No. i.) 

17. Plan and Bottom. — The drawing representing the top 
of an object is called the top view or plan, and that of the bottom 
is called the bottom view or bottom. Plan and bottom are views 
in which all the lines of sight are parallel, vertical lines. 

Plan and bottom are at right angles to elevations, and vice 
versa. Plan and bottom should always be between the same 
limiting pair of vertical lines with an elevation. The plan may 
be in line with one elevation, and the bottom view in line with a 
different elevation and the drawing be correct, though usually 
they are in line with each other and with the front elevation. 

A name has now been given the drawing of each face of an 

object, though a plan and one or two elevations are quite sufficient 

. to represent simple, solid objects. To represent objects with 

"interior features," it is necessary to add other views than those 

given above, views called "sections." 

18. Sections. — To section means to separate by cutting, the 
"section" being that portion cut; in mechanical drawing, a 
section is a drawing of the cut portion. 

Sections may be divided into three general classes: (1) longi- 
tudinal sections, (2) transverse sections, and (3) angular sections. 
These may be divided into full, half, and detail sections. 

19. Longitudinal Section. — A longitudinal section is a sec- 
tion in the direction of the length of an object and may be hori- 
zontal (cut on a horizontal plane), vertical (cut on a vertical plane), 
or angular (being cut on a plane at some intermediate angle) . 

20. Transverse Section. — A transverse section is a section 



ELEMENTARY PRINCIPLES AND DEFINITIONS. 9 

at right angles to a longitudinal section, and may be horizontal, 
vertical, or angular according to the position of the plane on 
which it is cut. 

21. Angular Section. — An angular section is any other than 
a longitudinal or transverse section. 

22. Full Section. — A full section is a section made by cutting 
entire and in one plane, that is, by cutting in two . 

23. Half Section. A half section is a section made by cut- 
ting in two planes at right angles, that is, by cutting out one 
quarter. 

24. Detail Section. — A detail section is any specially taken 
section. 

25. Explanatory of Sections. — Plate No. 2. Fig. 1 is a mechan- 
ical drawing (plan and elevation) of a rectangular pyramid, the 
dotted lines representing a hole in it — "interior features." Fig. 2 
is a full, longitudinal section, the drawing being a plan and ele- 
vation of one- half of the pyramid and showing only visible lines. 
Fig. 3 is a similar drawing of a half, longitudinal section of the 
pyramid. Fig. 4 is a plan and elevation of a full, transverse 
section, and Fig. 5 a like drawing of a half, transverse section 
of the pyramid. Fig. 6 is a plan and elevation of a full, angular 
section, the inclined line (A-B) across the elevation indicating 
the plane on which the section is taken; the view between 
the plan and the elevation is a drawing of the cut portion 
and is the conventional method of representing such sections. 
Fig. 7 is a left and front elevation of a hollow tube, the lined 
portion in the right end of the front elevation being a conven- 
tional method of indicating a full, transverse section. The 
lower portion of the drawing represents a horizontal, full, longi- 
tudinal section and is a front- and end-view drawing. Fig. 8 
depicts a full, transverse section, and a full, detail, longitudinal 
section showing the manner in which the two pieces are held 
together. Fig. 9 is a front and side elevation of a small, three- 
armed hand- wheel; the drawing at the right being a side eleva- 
tion, sectioned, and being cut in two, is a full, sectional eleva- 
tion ; the left figure illustrates the use of detail sections. Fig. 10 



IO 



MECHANICAL DRAWING. 



PLATE No. 2. 












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ELEMENTARY PRINCIPLES AND DEFINITIONS. II 

shows a half, sectional elevation, and Fig. n another example 
of detail sectioning. 

26. Drawing Sections. — In drawing sections it is customary 
not only to draw the cut portion, but also all points and lines that 
are visible when viewing the section; however, it is allowable, 
and often quite convenient, to draw the cut portion only. 

27. Arrangement of Sections on the Drawing. — It will have 
been noted that the plan, elevations, and bottom view have 
specially assigned positions on the drawing. The drawing of 
sections, in so far as possible, should be placed as follows: All 
sections taken on a horizontal plane, conventionally indicated 
by a horizontal line (usually a horizontal center line), should be 
placed either above or below the view sectioned. All sections 
taken on a vertical plane, conventionally indicated by a vertical 
line (usually a vertical center line), should be placed either to 
the right or to the left of the view sectioned. All sections taken 
at an angle, conventionally indicated by a straight line drawn 
through the portion to be sectioned, should be placed at right 
angles, either way, to the line (plane) on which the section is 
taken — the general rule being to assume the section as taken, 
that is, the object as having been cut at the proper place, and 
calling this a front elevation, to draw a plan, bottom, or side 
elevation, as the case may warrant, of the cut portion. 

Sections are usually indicated as being cut portions by cer- 
tain conventions applied to the drawing, the most common of 
which is a process called '* cross-hatching." 

28. Cross-hatching. — In drawing, to cross-hatch means to 
rule the drawing with straight lines, usually at forty-five degrees 
to the horizontal, thus indicating that the drawing is a repre- 
sentation of a cut portion and, at the same time, indicating the 
kind of material by the arrangement of the lining — different 
materials being represented by different cross-hatchings. (See 
Standard Cross-hatchings, page 179.) 

When two pieces of the same material are shown together 
in a drawing, the cross-hatching should have different directions, 
being usually " hatched" at right angles. When three or more 



12 MECHANICAL DRAWING, 

pieces of the same material are shown together, no two pieces 
should have the same angle and direction. When two pieces of 
different materials are shown together, the distinction is indicated 
by the different lining, though it is desirable to make the drawing 
more readable by changing the direction of the cross-hatching 
also. When three or more pieces of different materials are shown 
together, it is best to have a new direction for the cross-hatching 
of each. 

29. Lines. — Since drawings consist of different kinds of lines 
it is well to give a specific name to each kind. 



LINES AND THEIR WEIGHTS.. 



LINES OF THE DRAWING. 

Full. Dashed Dotted. 



Light. 




Medium 




Heavy. 




Center 1 


ines. 


Section 


lines 



Lighter than lines of the drawing. 



Heavier than lines of the drawing. 



Dimension lines. 



Lighter than lines of the drawing. 



Border lines, top and left hand lines to be of medium weight, 
bottom and right hand lines to be heavy lines. 



30. Lines of the Drawing. — Those lines which go to make 
up the drawing of an object are called lines of the drawing and 
may be either full or broken lines, light or heavy, entire or in 
combinations. 

31. Border Lines. — Border lines are lines which are drawn 
about a drawing inclosing it after the manner of a picture-frame, 
and are usually straight lines forming a rectangle. They vary 
greatly, however, as border lines are often of original design. 

32. Center Lines. — Center lines are broken lines drawn 
through the center of a drawing or drawings, as the case may 



ELEMENTARY PRINCIPLES AND DEFINITIONS. 



13 



be, and are used to "align" the different views — to produce 
an axis of symmetry. When two center lines are employed, they 
are usually at right angles, one being horizontal and one vertical. 
Center lines are used only on such drawings as naturally seem 
to require them, that is, on drawings of turned work and on those 
which can be symmetrically divided by such lines. (See Figs. 
5 and 6.) 




Fig. 5 
Such Drawings require the Use of Center Lines. 



V 







/ 

\ 











Fig. 6 
Such Drawings require no Center Lines. 



33. Section Lines.— Section lines are broken lines carried 
through the drawing to indicate the line (plane) on which the 
section has been taken— the line on which the object has been 
cut. 



14 MECHANICAL DRAWING. 

34. Construction Lines. — Construction lines are auxiliary lines 
used in the construction of the drawing and usually do not appear 
on the finished drawing. 

35. Projection Lines. — Projection lines are construction lines, 
usually horizontal or vertical, or both, and are used to project 
from one view to another. The horizontal limiting lines for all 
elevations and the vertical limiting lines for plan, elevation, and 
bottom are examples of projection lines. 

36. Dimension Lines. — Dimension lines are broken lines ter- 
minating in arrow-heads which, together with figures, when 
added to the drawing enable the observer to read the sizes of 
the various parts. 

37. Guide Lines. — Guide lines are light pencil lines used as 
guides in lettering. 

38. Light and Shade. — Without light and shade a drawing is 
merely a flat outline. It is often necessary and at times quite 
desirable to give the drawing some projection, to cause it to "stand 
out" from the paper, to give it relief, in which case it is neces- 
sary to introduce light and shade; this is called "shading the 
drawing." 

The shading of drawings is rarely resorted to for drawings 
representing flat surfaces, being most helpful when applied to 
drawings representing curved surfaces. 

39. Line Shading. — Line shading is lining the drawing with 
lines of varying weights and spacings. 

In all drawing the rays of light are assumed to strike the plane 
of the paper at an angle of forty-five degrees, usually taken as 
coming from the left. If a surface is uniformly covered with 
light, it is said to be in the light; if uniformly covered by a shadow, 
it is said to be in the shadow. From the former to the latter 
there are all degrees of light and shade — from that point at which 
the rays of light are reflected by the object to the observer's eye, 
which is called the brilliant point, to that point from which all 
rays of light are obscured. 

40. Shade or Shadow Lining. — Shadow lines are lines repre- 
senting those surfaces of an object which are in the shadow. The 



ELEMENTARY PRINCIPLES AND DEFINITIONS. 



*5 



application of shade or shadow lines to drawings is the practical 
method of "shading" drawings, the convention being as follows: 
Assume the drawing to be the object itself, and assume the parallel 
rays of light to extend across the plane of the paper and as coming 
from the upper left-hand direction, that is, from the top and left 
sides of the paper; then make those lines heavy which represent 





Fig. 7 Fig. 8 

Lines of Uniform Weight. Shade Lined. 

A Mechanical Drawing of a Flat Plate. 





Fig. 9 c „- 

Fig. 10 

Lines of Uniform Weight. Shade Lined* 

A Mechanical Drawing of a Ring. 

surfaces from which the light is excluded — a process which is 
sometimes called "back-lining." (See Figs. 7, 8, 9, and 10.) 

It is obvious that the right-hand and bottom lines, for draw- 
ings representing solid objects, and the upper, or top, and left-hand 
lines, on drawings of interior features — holes, etc. — are the proper 
lines to shade. 



i6 



MECHANICAL DRAWING. 



41. Drawing to Scale. — In mechanical drawing the drawings 
are usually drawn to scale, that is, the drawing is made to be 
of the same size as the object or some proportional size thereof. 
When possible it is best to make the drawing full size — the same 
dimensions as the object; in any case, however, it is well to 
choose such a scale as will make the drawing as large as possible. 
The usual scales are full size, three- fourths size, one-half size, and 
one-quarter size for comparatively small objects, and for those 
of large dimensions one- eighth size, one- twelfth size, one- six- 
teenth size, one-twenty-fourth size, one- thirty- sixth size, one- 
forty-eighth size, etc. 

42. Choosing the Scale. — In choosing the scale for any partic- 
ular-drawing there are three things to be considered: (1) the 




THE. OBJECT TO BE PRAWN^ 
Fig. 11 



dimensions of the object to be drawn, (2) the dimensions of the 
sheet of paper on which the drawing is to be made, and (3) the 
number of views to be drawn. With these known we have the 
full size of the drawing known, not only of any one view alone, 
but of the several views collectively — the mechanical drawing of the 



ELEMENTARY PRINCIPLES AND DEFINITIONS. 



17 



object — and the size of the sheet of paper to receive the drawing; 
it is then a simple matter to calculate the largest scale possible 
to fit the conditions. 

Example. — Let Fig. 11 represent the object to be drawn, let 
Fig. 12 represent the sheet of paper to receive the drawing — it 



.__!<£_ 



—1-1- 



OS QO 



THE SHEET TO RECEIVE 
THE DRAWING 



f 



TITLE 



Fig. 12 



being the standard sheet for the exercises of the Course — and 
let it be required to draw three views: (1) a plan, (2) a side eleva- 
tion, and (3) an end elevation. 

Assuming the object to be inclosed within a rectangular box 
as indicated by the figure A-B-C-D-E-F-G-H, note that the plan, 
or top view, is inclosed within a rectangle which is 2o // Xn" in 
dimensions, that the side elevation is inclosed within a rectangle 
the dimensions of which are 2o"Xi2", and that the end elevation 
is inclosed within an n"Xi2" rectangle. (See Fig. 13.) 

As to arrangement, it is fundamental, of course, that the 
long dimension of the drawing should be placed according to 
the long dimension of the sheet to receive the drawing; this 
dimension (of the drawing) is the sum of the length of the side 
elevation and the width of the end elevation and is 31". The 
short dimension of the drawing is the sum of the height of the 
side elevation and the width of the plan and is 23". A full-size 
drawing, then, would occupy a space 3i"X23 / '; the space to 
receive the drawing is 8"Xn". With these figures known it is 



x8 



MECHANICAL DRAWING. 



a simple problem in arithmetic to reduce the dimensions of the 
full-size drawing to fit the paper; the largest size possible is 



B 



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Fig. 13 


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evidently one-quarter size, 7l"X5f", and to fit the conditions 
let the drawings be arranged as in A, Fig. 14. 



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16 



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Side El. ! 



4 
End El. 



16 



G G 

B 



H 



Plan <? 

1 



Title 




Fig.. 14 



B 



43. Balance and Symmetry of a Drawing. — A correct me- 
chanical drawing of an object can be made and yet not present 
a very good appearance. The appearance of a drawing is a 
large measure of its value, and the draughtsman who would be 
successful should exercise due care to execute well-appearing, 
correct drawings. 

The essentials for a well-appearing drawing are: a neat, 
clean-cut drawing of the various views, neat and well-made 



ELEMENTARY PRINCIPLES AND DEFINITIONS. 1 9 

lettering, the dimensions carefully planned, and the whole so 
placed on the paper as to present a well-balanced effect with 
respect to the border lines and with one another, and a symmetry 
with any and all center lines that may be used on the drawing. 

A careful draughtsman will calculate the "balance" of his sheet 
— the space between views and between the drawing and the 
border lines — before beginning the drawing, a good general rule 
for which is as follows: First decide upon the number of views 
to be drawn; second, decide upon the arrangement of the views; 
third, calculate the space required for the drawing; fourth, 
ascertain the dimensions of the sheet of paper to receive the 
drawing; fifth, subtract the dimensions of the space required 
for the drawing from those of the space available; and sixth, 
divide the remainders by the number of the respective spaces 
to be provided. 

Example. — Let it be required to calculate the "balance" for 
the conditions given in the example of section 42. To begin 
with, the space required for the drawing (7f"X5f")> the space 
available (8" X 11"), and the arrangement of the views (A 9 Fig. 14) 
are known. 

An inspection of the arrangement shows that there are three 
spacings each way (horizontally and vertically) to be provided: 
(1) a space between views and (2 and 3) a space between the 
drawing and the border line of the sheet. To get the horizontal 
spacing, subtract the horizontal dimension (7f") of the drawing 
from the horizontal dimension (11") of the sheet and divide the 
remainder (3J") by three; when the remainder does not divide 
evenly, as in this case, a compromise may be arranged as is shown 
in Fig. 14. To obtain the vertical spacing, subtract the vertical 
dimension (5}") of the drawing from the vertical dimension of 
the sheet and divide the remainder (2\' f ) by three. 

44. Flexibility of the Drawing. — It seems, at first thought* a 
strange and very unnecessary procedure that certain rules be 
given for the proper arrangement of the views of a drawing, as 
has been done in the first part of these notes, and then to depart 
from their literal meaning, as is done in Fig. 14. 



£0 MECHANICAL DRAWING. 

The arrangement given in Fig. i, Plate No. i, is the proper 
and most clearly understood arrangement, and should be adhered 
to when possible. In the construction of a drawing, the limits 
of the paper and reserved spaces — space for title, notes, etc. — 
are important factors to be considered, and for the most economi- 
cal use of the sheet the drawing should be so made that it, to- 
gether with the lettering, the title and notes, will completely fill 
the sheet and the whole be made to present a full and well-bal- 
anced appearance. To do this it is often necessary to violate 
the given rules and to make the arrangement to fit the condi- 
tions — it must be flexible. 

A clear understanding of the rule is first necessary, and having 
the underlying principles well in hand it will always be a simple 
matter to adjust the drawing to fit any and all conditions and 
yet fulfill the requirements for a correct mechanical drawing. 
For this reason the rule is given and should receive due con- 
sideration. 

The first requirement of a mechanical drawing is to "show" 
the object, and any arrangement which does this clearly is a 
correct arrangement. 

45. Dimensioning. — Dimensioning is one of the most impor- 
tant and widely discussed details of mechanical drawing, each and 
every shop using that system which works out most satisfac- 
torily for its particular work. Some shops use the decimal sys- 
tem — "engineer's scale" (sect. 100) — giving the dimensions in 
hundredths parts of the unit used, as .09 of an inch, the inch being 
the unit.* Other shops use the "architect's scale," giving the 
dimensions as J inch, \ inch, J inch^ etc., the inch being the unit 
used, and this is the system most widely in use. Again, some 
shops — mostly in boiler- work — give dimensions in inches entirely, 
as 108 inches, while other shops use feet and inches, as 10 feet 
4 inches, which latter system is the one usually used, and this, 
in turn, is varied when the dimension to be given is an even 
number of feet, some draughting- rooms — notably those of bridge 

* This explanation is with reference to American practice, the inch being the 
unit adopted in the United States. 



ELEMENTARY PRINCIPLES AND DEFINITIONS. 21 

and plate works — giving it as 19 feet o (zero) inches, and others 
— manufacturers of machinery — simply 19 feet, no mention 
being made of the inches. It is universally agreed, however, 
that all dimensions under three feet should be given in inches, 
and those greater than three feet to be given at the draughts- 
man's discretion. 

In most shops certain notation is used to indicate feet and 
inches, some shops using the abbreviations "ft." for feet and 
"in." for inches; others use one dash, thus ', for feet, and two 
dashes, thus ", for inches, while some shops give all dimensions 
in inches and with that understanding omit all such notation. 
Another method is to write "ft." for feet and use the two dashes 
(") for the inches. The dashes for both feet and inches is the 
usual practice. 

In putting on dimensions those figures representing the full 
size of the object are given and a note added as to the scale of 
the drawing, and not figures representing the size of the drawing 
unless it be a full-size drawing, when, of course, the dimensions 
of the drawing and of the object are the same; in any case a note 
as to the scale used should be on the drawing. 

46. Selection of the Necessary Views. — Thus far six views 
of an object have been dealt with: plan, front, right, left, and 
rear elevations, and bottom view. Very rarely is this number 
necessary to show an object: a lesser number being usually suffi- 
cient. The selection of the proper views and their number is of 
primary importance, and it is here that the draughtsman must 
exercise his ingenuity and knowledge of shop practice. First of 
all the drawing must tell the story, it must clearly show the object, 
and the least number of views which does this is the correct 
number to use. 

In the selection of what views should be drawn the draughts- 
man should consider the purpose of the drawing. If it is for shop 
purposes — a shop drawing — it should be complete in every detail; 
for example, if it be a drawing of a single piece of a machine— a 
detail — the draughtsman should place himself in the shopman's 
position and should consider just what is necessary to show 



22 MECHANICAL DRAWING. 

the piece, what would he have to know to produce it, what 
views are necessary to portray every feature, what dimensions, 
what notes, etc. If it be an assembled drawing for erectional pur- 
poses, let the draughtsman assume the position of the erecting 
workman, and consider what drawings, dimensions, notes, etc., 
would be necessary to carry out the work. 

47. Usual Number of Views. — For simple objects, a plan, 
one elevation and a sectional view, or two elevations and a section, 
properly noted and dimensioned, is all that is necessary to clearly 
define the object. For complex objects the views range in num- 
ber from either of the above combinations to a drawing composed 
of a plan and bottom view, four elevations, and any number of 
sections. 

48. Use of Dashed and Dotted Lines to Reduce the Number 
of Views. — In manufacturing the draughting-room is a means to 
an end. From the draughtsman's standpoint the number of 
views constituting a drawing should be as small as possible; 
from the workman's — the shopman's — standpoint the drawing 
should be as elaborate and complete as possible. A mean of these 
two extremes is the usual practice, and to assist the draughtsman he 
is allowed to use dashed and dotted lines to indicate hidden features. 

The compromise is quite satisfactory for comparatively simple 
objects and oftentimes may decrease the labor of making a legible 
drawing by one-half; it is, however, very desirable that dashed 
and dotted lines be reserved for simple drawings, as for the more 
elaborate ones they prove very confusing; in such drawings they 
should be omitted and other views and sections added . 

49. Beginning to Draw.— When a drawing is to be made, the 
first thing to be considered is the purpose of the drawing; with 
this well in mind carefully study the object to be drawn and 
decide upon the least number of views it will be necessary to 
draw to clearly define the object. Having decided upon the 
number of views to be drawn, consider the size of the sheet of 
paper to receive the drawing and, in accordance with section 42, 
select the largest scale possible under the conditions. With the 
dimensions of the drawings known, the margin between them 



ELEMENTARY PRINCIPLES AND DEFINITIONS, 23 

and the border lines and the spaces between one another may be 
calculated and the drawing balanced without a line ? being drawn; 
this done the drawing may be begun. Do all thinking and 
planning with few preliminary lines, know what to do, how it 
is to be done, and then proceed with the work. 

50. Draughting-room Practice. — In ordinary commercial 
draughting one meets with two kinds of mechanical drawing: 
(1) sketches which are used for preliminary purposes — temporary 
drawings — and (2) the valuable permanent drawings which are 
placed on file and carefully preserved. 

Sketches are usua ly made in pencil — though pen and ink 
are sometimes used — and are usually free-hand drawings. The 
permanent drawings are constructed with a view to reproduction, 
the usual procedure being as follows: 

A pencil drawing is first carefully constructed on some medium 
grade of paper, and from this pencil drawing a tracing is made 
in water- proof ink on tracing-cloth, or tracing-paper (the former 
is preferable), and from this tracing a blue-print is made. 

Draughting- rooms are like individuals, each has its own 
particular method for the accomplishment of its purpose, the 
purpose of a draughting-room being, primarily, to construct draw- 
ings; all, however, agree on a general method of procedure which 
may be condensed to the following: 

Drawings must be clear and concise. 

Drawings must be complete. 

Drawings should have all dimensions given-— total dimen- 
sions and of all parts — no addition, division, or subtraction being 
left to the shopman. 

Drawings should be confined to small sheets. 

Drawings should be grouped, that is, things of a kind should 
be placed on a sheet of the kind; as, drawings of pieces to be 
forged should be placed on a " sheet of forgings"; all brasswork 
should be together, all cast-iron parts should be drawn by them- 
selves, etc. 

Draughtsmen should show a knowledge of the work they 
propose; how each piece is to be produced; as, holes to be cored 



24 MECHANICAL DRAWING. 

should be so marked; holes to be drilled should be marked "to 
be drilled"; holes to be drilled and tapped should have* the size 
of drill and tap given; surfaces to be finished should be marked 
"to be finished"; the number wanted of each piece and kind of 
material should be noted, etc. 

51. The Time Element in Drawing. — Rapid execution of 
drawings is demanded by all firms, and the ability to execute a 
clean-cut, well-appearing drawing within a short time is the 
measure of a draughtsman's worth. The beginner should remem- 
ber the value of time in the execution of his work and should 
strive to produce a legible drawing in the shortest time possible; 
this, however, not to be at the expense of the quality of the work. 
Quality without quantity means limited pay and a secondary 
position; quantity without quality is a similar condition; while 
quantity and quality is the correct combination and means the 
highest salary and most responsible position. 

In acquiring the art of draughting careful search should be 
made to find ways, means, and "kinks" with which to expedite 
the work if possible. Of these "labor-saving devices," besides 
special tools and other mechanical means, mention may be made 
of free-hand lettering and of certain conventions, some of which 
are universally adopted and others which pertain to a particular 
line of work. 

Free-hand lettering being so far in advance of mechanical 
lettering as regards time required in its execution needs no other 
argument as to the "why" of its desirability. 

The laborious, time-consuming, and erstwhile universal method 
of cross-hatching sections with lines in certain arrangements to 
indicate cut portions and kinds of materials is, of late years, being 
discarded in a large number of shops for other conventions 
more convenient and rapid of application. Some shops use no 
cross-hatching whatever, simply marking the drawings C. I. for 
cast iron, W. I. for wrought iron, S. for steel, etc., and indicating 
cut portions by darkening that portion of the drawing with a 
lead-pencil or other quickly applied medium, as by coloring the 
sections with brush and water colors. 



ELEMENTARY PRINCIPLES AND DEFINITIONS. 2$ 

There are a great number of minor labor-saving kinks, many 
presenting themselves to ingenious draughtsmen, but to the 
student suffice it to again advise a sharp outlook for these things. 

52. Conventions. — To construct every detail of a drawing 
theoretically exact would consume much valuable time, and to 
expedite the work certain conventions are adopted. Every class 
of drawing — bridge drawing, the drawings used in electrical work, 
etc. — has its particular and peculiar conventions; also, different 
firms engaged in the same fine of work often use conventions 
peculiar to themselves. There are, however, a large number of 
simple conventions — fundamentals — such as screw-threads, breaks, 
methods for indicating sections, the kind of material, etc., that 
are common, with possibly slight variations in certain cases. A 
number of these are given in the accompanying drawings and 
should be noted. 



CHAPTER II. 

LETTERS, FIGURES, AND LETTERING. 

53. Fundamentals. — Lettering is to a drawing what clothes 
are to a man — it makes the appearance, and appearance is of 
much importance to a drawing. A drawing may be correct in 
all its details and yet present a poor appearance, but a well- 
appearing, correct drawing is what manufacturers want and are 
willing to pay for; therefore the ability of a draughtsman to do 
good lettering is a measure of his worth. The study of lettering, 
then, becomes of prime importance to the student of mechanical 
drawing. 

A drawing may be "made or marred" in the lettering, hence 
great care should be exercised in the lettering of it, and that letter 
which can be most rapidly made, which looks well when made 
and in any size, should be selected for the work. A letter to fulfill 
these conditions must, obviously, be one of simple outline, thus 
minimizing and expediting the labor of its execution, and being 
free from ornamentation it presents a clear outline and is readily 
legible. 

The letter most widely accepted as meeting these conditions 
is what is known as the "Gothic Alphabet." Of this letter there 
is the upper case, or capital letters, and the lower case, or small 
letters; these may be vertical or inclined, which gives practically 
four alphabets and is quite sufficient for all usual commercial 
draughting. 

The Gothic alphabet may be constructed free-hand or with 

instruments, and may be a single-line letter or a heavy letter 

made up of heavy lines, several "single" lines in thickness. To 

construct the letters with instruments — mechanically — consumes 

26 



LETTERS, FIGURES, AND LETTERING. 27 

too much time for practical work and the beginner should devote 
his attention to the free-hand alphabet. 

To acquire the ability to execute neat and well-appearing 
free-hand letters, the student should first carefully study the 
standard proportions and characteristics of the various letters 
and then practice their construction. Much care and pains must 
be taken with these preliminaries, as lettering is an art which 
cannot be mastered in a few hours, but requires perseverance 
and practice. When the individual letters have been mastered 
to a degree, the construction of words may be taken up. 

The spacing of the various letters which go to make up a 
word now enters into the subject and is a very important factor. 
The letters should be placed as near one another as is consistent 
with clearness (about one- sixteenth to one-sixty- fourth of an 
inch apart), thus giving the arrangement a well-grouped and 
compact appearance. Each letter should be of the same alpha- 
bet — upper or lower case, vertical or inclined — of the same size 
(initial letters excepted) and uniformly spaced. Much considera- 
tion of the dimensions of the various letters, together with spacing 
and a large amount of practice, is necessary at this point. 

Having acquired the ability to execute words in a rapid, 
neat, and well- appearing manner, the student is ready to execute 
sentences, and now the spacing of words demands attention. 
Words should be placed according to the space they are to occupy; 
ordinarily, however, they should be from one- eighth to one- 
quarter of an inch apart, the letters of each word being so grouped 
that the words are quite compact, and this small space between 
words sufficient to cause them to stand out and be easily read. 

In all lettering much care should be exercised to produce a 
regular and uniform effect, that is, the individual letters of words 
should be neither cramped nor isolated, enlarged or decreased in 
size, but the whole so constructed as to secure a well-balanced 
and uniform word. This matter of regularity and uniformity 
is the "secret" of good lettering and applies not only to words 
but to entire sentences and groups of sentences as well. 

After the student has acquired a working knowledge of the 



28 



MECHANICAL DRAWING. 




foregoing fundamental requirements, from thence on his letter- 
ing becomes a matter of practice, and as "practice makes perfect" 
too much time cannot be devoted to it. 

54. A Study of Letters. — Taking up the upper- case Gothic 
Alphabet, attention should be given to the proportions and char- 
acteristics of each letter, together with the manner of its con- 
struction. The most popular style of this alphabet is the " square" 
letter, so called because the major portion of the alphabet may 
be constructed within a square. 

The vertical type of the upper- case, square Gothic alphabet 
is used for illustration, though the remarks given apply, also, 
to the inclined type of the same alphabet. 

The letter A, constructed in the manner indicated — 
the arrows indicating the direction of the stroke and 
the figures the order in which the strokes are made — 
has equal width and height for proportions, and is 
characterized by the horizontal bar, stroke 3, which is 
below th2 horizontal center line through the square. 
In the inclined letter, alphabet No. 3^ Plate No. 3, 
note that stroke 2 is vertical. 

Proportions, the height equals the width; char- 
acteristics, bars 2, 3, and 6 are horizontal, the upper 
part of the letter is smaller than the lower part — 
stroke 3 is above the center of the square — and arcs 4 
and 5 are arcs of circles. In the inclined letter strokes 
4 and 5 are elliptical arcs. 

Proportions, the height equals the width; char- 
acteristics, all of the arcs are circular arcs, and the 
lower terminus of the letter extends farther to the 
right than the upper terminus, thus giving the letter a 
kind of base. In the inclined letter the arcs are 
elliptical. 

Proportions, the height equals the width; char- 
acteristics, bars 2 and 3 are horizontal, and stroke 4 
is the arc of a circle. In the inclined letter this stroke 
is the arc of an ellipse. 




€ 


3\ 




LETTERS, FIGURbS, AND LETTERING. 



29 



2 , 



-f 







d 


\ 




ll 










Proportions, the height equals the width; char- 
acteristics, three horizontal bars, the bottom bar 
slightly longer than the upper bar — to give the letter 
a base — and bar 3 is above the center of the square 
and from one half to two- thirds the length of the top 
bar. 

Proportions, the height equals the width; char- 
acteristics, bars 1 and 2 are equal in length, and bar 3 
is above the center of the square and from one-half 
to two- thirds the length of bar 2. 

Proportions, the height equals the width; char- 
acteristics, the arcs are arcs of circles, bar 2 is on 
the horizontal center line and extends a trifle to the 
right of the terminus of arc 3. In the inclined letter the 
arcs are elliptical. 



4 




Proportions, the height equals the width; char- 
acteristics, the side lin s are parallel, and the cross-bar 
is above the center of the square. 

Proportions, the height equals the height of the 
square; the width equals the width of the line. (Note 
that I is the first letter in which the height and the 
width are unequal.) Characteristic, it is a simple 
straight line. The upper-case I is not dotted. 

Proportions, the height equals the width; char- 
acteristics, the arcs are the arcs of a circle, and the 
left terminus does not extend quite up to the center 
line. The letter J is often misconstructed, being 
sometimes turned backwards; also, one is apt to make 
it too narrow and thus spoil its proportions; care 
should be exercised not to extend the left-hand ter- 
minus, stroke 2, above the center line, else the letter 
will be confused with the letter U. In the inclined 
letter the arcs are elliptical. 



3° 



MECHANICAL DRAWING. 




\ 








1 

' 2 






— > 






™« 







Proportions, the height equals the width; char- 
acteristics, bar 2 extends from a point not quite to 
the corner of the square to a point below the inter- 
section of the center line of the square and the vertical 
bar. Bar 3 joins bar 2 above the center and extends 
to the lower corner of the square. 

Proportions, the height equals the width; char- 
acteristics, bars 1 and 2 are of equal lengths and occupy 
two sides of the square. This letter is sometimes 
made backwards. Note the proper way of drawing 
bar 2. 

Proportions, the width is from one-fourth to 
one- third greater than the height of the letter, 
making M the widest letter thus far; character- 
istics, the side lines are parallel and the diagonals, 
3 and 4, are of equal lengths. This letter is often 
made as the letter W would appear if inverted, 
and when so constructed is incorrect. 

Proportions, the height equals the width; char- 
acteristics, the side lines are parallel and the diagonal 
extends from the upper left-hand corner of the square 
to the lower right-hand corner. 

Proportions, the height equals the width; char- 
acteristic, it is a complete circle. In the inclined 
letter it becomes an ellipse. 

Proportions, the height equals the width; char- 
acteristics, strokes 2 and 3 are horizontal, the lower 
one, 3, is below the center of the square, and the arc 
is the arc of a circle. In the inclined letter the arc is 
elliptical. 

Proportions, the height equals the width; char- 
acteristic, it is a complete circle, same as the letter O 
with the addition of stroke 3. In the inclined letter 
the circle becomes an ellipse. 



LETTERS, FIGURES, AND LETTERING, 



31 





r 






Proportions, the height equals the width; char- 
acteristic, it is the same as the letter P with the addi- 
tion of stroke 5. The letters P and R are two of the 
"hard" letters to construct; do not fail to note the 
two horizontal bars, the lower one being below the 
center of the square. 

Proportions, the height equals the width; char- 
acteristics, the arcs are the arcs of ellipses, and the 
upper part of the letter is smaller than the lower part. 
The letter S is the "hardest" letter to construct, and 
is often turned backwards; note the proper "turn" 
and that the upper part of the letter is smaller, in two 
directions, than the lower part. 

Proportions, the height equals the width; char- 
acteristics, the two bars are of equal length — equal to 
the length of a side of the inclosing square — and the 
vertical bar, 2, is in the center of the square. 

Proportions, the height equals the width; char- 
acteristics, the side lines are parallel and the arcs are 
arcs of a circle. Care should be exercised to always 
make the letter of full width, as the tendency is to 
construct a letter of "under width." In the inclined 
letter the arcs are elliptical. 

Proportions, the height equals the width; char- 
acteristic, it is the same as the letter A inverted; note 
the full width at the top — equal to the width of the 
square — do not make it less. In the inclined letter 
stroke 1 is made vertical. 

Proportions, the height equals the height of 
the square and the width is from one-half to 
^ three-fifths greater than the height of the letter 
— the letter W is the widest letter in the alphabet; 
characteristic, alternate lines are parallel — it 
can be said to be made up of two Vs. The 
letter M is often inverted for the letter W; this 
is incorrect. In the inclined letter strokes 1 and 
3 are drawn vertical. 



MECHANICAL DRAWING. 




N 





Proportions, the height equals the width; char- 
acteristics, the width at the top is slightly less than 
the width at the bottom of the letter and the bars cross 
above the center of the square. 

Proportions, the height equals the width; char- 
acteristic, the three bars unite at the center of the 
square. Note that the full width of the square is 
■ necessary at the top; do not make it less. 

Proportions, the height equals the width; char- 
• v acteristics, the two horizontal bars are of equal lengths, 
and the diagonal, 2, extends from the upper right- 
hand corner of the square to the lower left-hand corner. 
The letter Z is often made backwards, bar 2 being 
turned the wrong way; note the correct slant. 

Proportions, the width is about one-fourth greater 
than the height; characteristic, it is the same as the 
6 figure 8 with the addition of strokes 5 and 6. 

55. Modifications. — The letters A, C, G, O, Q, V, and Y 

if made on the " square" plan will in some words appear to be 
smaller than other letters similarly constructed and require to 
be slightly modified to eliminate the optical illusion, in which 
case the following is recommended : 

Make the letter A to extend slightly above the other letters 
and to have a width at the bottom a trifle greater than the width 
of the side of the square. The same modification is given for 
the letter V, i.e., the width of the letter should be greater than 
that of the other letters, and it should extend below them. The 
letters C, G, O, and Q may be made slightly elliptical in shape, 
having a greater width than the side of the square. The letter 
Y may be given increased width across the top. 

The letters M and N are also susceptible to modification, 
though not for the same reason given above. To construct these 
letters as given, and secure good results, much care has to be 
exercised in drawing the diagonal lines, as any slight variation 
from the correct slant is at once apparent. The modification. 




LETTERS, FIGURES AND LETTERING. 



33 



PLATE No. 3. 




34 MECHANICAL DRAWING. 

of these letters given in alphabet No. 3, Plate No. 3, is recom- 
mended, being a style somewhat more easily constructed and 
looks well if not quite exact in all its lines. Care should be taken 
with the letter N not to make the diagonal bar too nearly a hori- 
zontal line, else the letter will become confused with the 
letter H. 

56. Suggestions. — It is recommended that the square letter 
be used for all practical and usual lettering, the modifications 
being introduced at the draughtsman's discretion. In cases where 
the square letter does not seem to meet the requirements, as, 
for example, when it is desired to occupy a large elongated space 
with a few words or when it is required to place a large num- 
ber of words in a comparatively small space, letters other than 
the square alphabet may be used to advantage — an " extended" 
letter being recommended for the former case and a "condensed" 
type for the latter case. (See pages ^>Z (bottom) and 181.) 

57. Combinations and Spacings. — As has been stated, to make 
printing "stand out" and be easily read, it is first necessary to 
make the words compact; second, the spacing must be uniform; 
and third, the letters must be of the same height — be even along 
the top and bottom. Some letters, because of their shape, when 
made and spaced in the usual way give an "open" appearance 
to words; to obviate this and to secure compactness, examples 
of various combinations of letters are given in Plate No. 3; also, 
examples of spacing — these should be carefully studied. 

58. Figures. — At the same time attention is being given to 
the upper-case alphabet some study should be given to the pro- 
portions and characteristics of figures, since figures are essen- 
tials of drawings. A drawing poorly figured — dimensioned — is 
like a drawing poorly lettered — the appearance is marred; how* 
ever, figures and letters go hand in hand, and a drawing poorly 
lettered is usually poorly figured, and vice versa; a draughtsman 
with the ability to do good lettering will usually do good figures. 

Like the letters the square type of figures is the most popular 
type, the standard proportions and characteristics being as 
follows : 



LETTERS, FIGURES, AND LETTERING. 



35 









The figure i made in the manner indicated has 
proportions, the height equals the height of the square, 
the width equals the width of the line; characteristic, 
it is a simple straight line. 

Proportions, the height equals the width; character- 
istic, the upper portion of the figure is larger than the 
lower portion. 

Proportions, the height equals the width; charac- 
teristic, the upper portion is smaller than the lower 
portion of the figure. 

Proportions, the width is about one-fourth greater 
than the height; characteristics, the short horizontal 
stroke at the top and the bar below the center of the 
square. The usual tendency is to make the figure 
of "short width" — it should be wider than it is high 
also, the stroke 3 is often made too high: note that \ 
is half w r ay between the horizontal center line ar.4 
the bottom of the square. 

Proportions, the height equals the width; charac- 
teristics, the upper portion of the figure is speller than 
the lower portion, and the arcs 2 and 3 are* elliptical. 

Proportions, the height equals the width; charac- 
teristics, the lower portion of the figure occupies over 
one-half of the square and is an ellipse; the upper 
part is parallel to the top line of the ellipse. 

Proportions, the height equals the width; charac- 
teristic, bar 2 does not extend out on the left even with 
bar 1. 

Proportions, the height equals the width; charac- 
teristic, the figure is made up of two ellipses, the upper 
ellipse being smaller than the lower one. 




3 6 MECHANICAL DRAWING. 



Proportions, the height equals the width; charac- 
teristic, the same as the figure 6 inverted. 



Proportions, the height equals the width; charac- 
teristic, it is a complete circle, the same as the letter O. 



As in lettering, there is the vertical and inclined type of figures, 
and the remarks on combinations and spacing given for lettering 
obtains for figures also. 

The extended figure — one in which the width is greater than 
the height — is a close rival of the square type, being easily con- 
structed and quite clear in outline. For some cases a condensed 
figure is found convenient; it is well, therefore, for the student 
to acquire the three [(i) square, (2) extended, and (3) condensed] 
types of figures. 

59. Fractions. — Examples of figures arranged into complex 
numbers are given in Plate No. 3, and should be carefully 
studied. 

In mechanical drawing always use "mechanical" figures — 
those given above — and in fractions make the dividing line between 
the numerator and the denominator to be a straight line in line 
with the dimension line. To insure clean-cut fractions, be sure 
to separate the figures so that they do not touch one another, 
particularly do not permit either the numerator or the denomi- 
nator to touch the dividing line. In complex numbers the whole 
number may be made from two- thirds to three- fourths of the 
height of the fraction. 

60. Lower-case Alphabet. — Thus far the upper-case alphabet 
has been discussed — figures being rated as of the upper case — 
and as these have to do with but titles and sub-captions, a letter 
is yet to be adopted for the notes of explanation which are 
necessary on drawings, and these notes usually represent the 
major portion of the lettering. 

For this work there are two very popular letters: (1) an upper- 



LETTERS, FIGURES, AND LETTERING. 37 

case alphabet of small dimensions, and (2) a lower-case alphabet, 
Fig. 15, the latter being somewhat more widely in use because 
of its ease and rapidity of execution. Of this letter there are the 
several styles, square, extended, condensed, vertical, and inclined. 

cib cdefcjhijklmn op qr stu v w x lj z 
abcdefghijklmnopqrstuvwxyz 

Fig 1 5. 

The proportions, characteristics, and manner of construction 
may be studied from alphabet No. 2, Plate No. 3. The general 
remarks on lettering, combinations, spacing, etc., apply to the 
lower-case alphabet; and lettering of this alphabet should be 
made accordingly. 

For the beginner it is best to first draw construction lines — 
guide lines— in pencil to block out the space for the letters, or 
to use coordinate ruled paper for his practice, and later to use 
only top and bottom guide lines, doing the spacing and pro- 
portioning " with the eye. " 

61. Mechanical Letters. — Plate No. 4 delineates the usual 
mechanical letters — letters made with instruments. The plain 
"block" letter (that shown in the top row) is the style most used 
and is the basis for nearly all plain and ornamental mechanical 
lettering. The plate is self-explanatory — adding here that the 
light construction lines should not appear in finished lettering — 
and should be given due consideration and study. 



38 



MECHANICAL DRAWING. 



PLATE No. 4. 




CHAPTER III. 

PROJECTION. 

62. Scenographic Projection.— To project means to plan, to 
scheme, to delineate, to draw the outline of a thing. In Fig. i, 
explanatory of the drawing of objects viewed from a finite dis- 
tance, the lines joining the several points of the object and the 
point of sight — there called lines of sight— may be said to project 
the image of the object on the retina of the observer's eye (one eye 
only being used, since but one point of sight is assumed), and 
the lines themselves, said to be lines of projection or projecting 
lines. If these lines be intersected by a plane and the points in 
which they pierce the plane be connected by straight lines, a 
drawing of the object will be obtained which is said to be pro- 
jected onto that plane; such a drawing — called a projection — 
is an example of scenographic projection. 

If ths intersecting plane be a plane perpendicular to the 
horizontal — a vertical plane — the drawing projected on such a 
plane is called a " perspective drawing" (Fig. 3). For example, 
let the student station himself before a window overlooking a 
street scene; then stretch a sheet of transparent paper over the 
glass, and choosing a point of sight — a view-point — look through 
the paper onto the scene; the picture will then seem to be pro- 
jected onto the paper, and if the lines be traced in with pencil 
or ink, the drawing thus obtained will be a perspective drawing, 
and the scene said to be shown in "perspective." 

In ordinary mechanical drawing objects are but rarely shown 
in scenographic projection or perspective. 

63. Orthographic Projection. — In mechanical drawing, as 
has been noted, the point of sight is assumed as being at an infinite 

39 



40 MECHANICAL DRAWING. 

distance from the object, and the lines of sight to be practically 
parallel. Following the same line of reasoning as given for sceno- 
graphic projection, if the lines of sight be intersected by a plane, 
and the points in which the lines of sight pierce this plane be 
joined, a drawing of the object will be obtained which is said to 
be projected onto the intersecting plane. If the intersecting plane 
be in a position which is perpendicular to the lines of sight, the 
projection on that plane is said to be an " orthographic projec- 
tion," Fig. 2. 

Orthographic projection is the more useful to the student 
in engineering, and will now be taken up in detail. 

64. The Planes of Projection. — Thus far we have treated of 
but one plane of projection — the intersecting plane. To apply 
orthographic projection in mechanical drawing, it is necessary 
to have more than one plane of projection, since, in such draw- 
ing, it is required to draw more than one view of the object; also, 
the position of a point, or object, in space cannot be fixed, save 
with reference to the one plane only which is insufficient for the 
purpose of use in mechanical drawing. All orthographic pro- 
jection, then, is reckoned with reference to two planes of pro- 
jection, two planes being the least number for practical work. 

The two planes assumed are (1) a horizontal plane, called 
the horizontal plane of projection, conventionally designated by 
the letter H, and called " plane i?," and (2) a vertical plane, 
called the vertical plane of projection, conventionally designated 
by the letter V, and called "plane V." These two planes of 
projection are assumed to be of infinite expanse, to intersect at 
right angles, and to divide space into four equal parts, called 
the "four quadrants." 

65. The Four Quadrants. — Let Fig. 1, Plate No. 5, repre- 
sent a limited portion of each of the two planes of projection 
(the drawing shows the planes to be of some thickness: the 
planes assumed, however, are mathematical planes and of infini 
tesimal thickness — practically of no thickness), A-B-C-D being 
the vertical plane of projection, V, E-F-G-H the horizontal 
plane of projection, iT, and X-Y the line in which the two planes 



PROJECTION. 



41 



PLATE No. 5. 




O 

c 
o 

"■+-» 
o 

<D 

• —\ 

o 
CL 

o 

_c 

a 

i— 

bO 
o 

_c 

+-» 

1— 

O 

<o 

_c 

H 



(D 

C 



tf 



OQ > 
8 



8 


\o 


/ 


< X 


s 

I 



00 
U. 





ID 







8) 




** 






c 






X 






"0 














CL 


00 




> 









C3 









81 




* 




e< 









< 




X 




i 





42 MECHANICAL DRAWING. 

intersect, being the "ground line" — conventionally designated 
by the letter G. With the planes viewed as shown, the four 
quadrants are numbered counter-clockwise, that in front of 
the vertical plane and above the horizontal plane of projection 
being the first quadrant, that behind the vertical plane and above 
the horizontal plane the second quadrant, that space below H 
and behind V the third quadrant, and that below H and in 
front of V the fourth quadrant. 

It should be noted that the planes of projection are viewed 
from two positions only: (i) looking down as indicated by the 
arrows V, V, and (2) looking horizontally as indicated by the 
arrows H, H. With reference to H and V, the projecting lines 
used for projecting points and lines onto these planes are 
respectively parallel to these two directions of sight; that is, one 
looks vertically down upon and projects perpendicularly onto the 
horizontal plane, and looks horizontally upon and projects per- 
pendicularly " against" the vertical plane of projection. 

66. The Projection of a Point, with the Planes V and H at 
Right Angles. — Let P, Fig. 1, Plate No. 5, represent a point in 
space; to find its horizontal projection, drop the perpendicular 
P-p to the horizontal plane, and the point p, in which this per- 
pendicular pierces the plane, is the horizontal projection of the 
point P. To find its vertical projection, erect the perpendicular 
P-p' to the vertical plane, and the point p', in which this per- 
pendicular pierces V, is the vertical projection of the point P. 
These two projections, p and p', fix the position of the point P 
with reference to the planes V and H; for, given p and p r , by 
erecting perpendiculars to the planes V and H, the two per- 
pendiculars will intersect at P and thus define the position of 
the point. 

The student should also note that the perpendicular P-p to 
the plane H shows on the vertical plane as the line p'-o, for 
to obtain the projection of a straight line it is but necessary to 
project any two points of the line and join their projections. In 
this case the two points taken are the two extremes, P and p 
(this is the usual method of projecting a definite portion of a 



PROJECTION. 43 

line), p' being the vertical projection of P, and o the vertical pro- 
jection of p\ also, the horizontal projection of the projecting line 
P-p f is p-o. It is obvious that p-o and p'-o are perpendicular 
to each other, being adjacent sides of the rectangle P-p-o-p' '. 

67. The Planes V and H Revolved. — If compelled to con- 
struct all projections with the planes V and H in their true posi- 
tions — V, vertical, and H, horizontal — the task would be entirely 
too laborious and time-consuming for practical use. That the art 
may become practical, the vertical plane is assumed to be revolved 
into coincidence with the horizontal plane, thus forming but one 
plane; and assuming the plane of the paper to be a limited portion 
of this plane, the problem is solved. 

Explanatory. — Plate No. 5. Let Fig. 1 represent a limited 
portion of the planes V and H, and let the plane V (A-B-C-D) be 
revolved in the direction of the arrows (counter-clockwise) until 
it becomes coincident with the plane H (E-F-G-H). Fig. 2 
represents an intermediate position of V in its revolution, and 
Fig. 3 the coincident position. Now, assume the planes as 
depicted in Fig. 3 to be picked up and " squared about," pre- 
senting themselves as shown in Fig. 4. Considering the first 
quadrant, it will be noted that the vertical plane falls above the 
ground line and that the horizontal plane falls below the ground 
line. The first quadrant, only, is considered in the following dis- 
cussion. 

[To facilitate his conception of the following projections, the 
student is advised to construct a pasteboard or wooden model of 
the planes V and H, capable of being revolved. Take two pieces 
of pasteboard about six or eight inches square, cut a straight slot 
half way across the middle of each and put the two pieces together, 
slot to slot, and press ''home"; this will give a model which 
revolves into one plane, approximately.] 

68. The Conventional Projection of a Point. — Plate No. 5. 
Referring again to Fig. 1 depicting the projection of the point P, 
it is obvious that the figure P-p-o-f is a rectangle whose plane is 
both perpendicular to the planes V and H, and to their inter- 
section, X-Y. Now as the planes of projection are revolved into 



44 MECHANICAL DRAWING. 

coincidence, note the revolution of the projections of the point P 
(Figs. 2, 3, and 4) and it is seen that the two projections are in the 
same straight line perpendicular to the ground line. The student 
should also note that the distance of the point P from the vertical 
plane is shown on the horizontal plane by the perpendicular 
p-o; also, that the distance of the point P from the horizontal 
plane is shown on the vertical plane by the perpendicular p'-o\ 
from which is deduced, the distance of a point from the vertical 
plane of projection is measured on the horizontal plane, and the 
distance of a point from the horizontal plane of projection is 
measured on the vertical plane. 

As has been stated, the planes V and H are assumed to be 
of infinite expanse, and instead of considering definite portions 
of these planes, as has been done thus far, for practical work the 
planes are assumed by simply drawing the ground line X-Y, and 
when considering the first quadrant only — as is here done — 
understanding that all the space above X- Y represents the vertical 
plane, V, and all of the space below X-Y represents the hori- 
zontal plane, H. The conventional projection of the point P, 
then, is shown by Fig. 5. 

69. The Conventional Assumption of a Point. — Plate No. 5. 
A point is assumed by its two projections (one projection does 
not fix the position of the point, two are necessary); also, these 
two projections always lie in the same straight line, perpendicular 
to the ground line. 

Let it be required to assume a point P, four inches from the 
vertical plane of projection, and ten inches from the horizontal 
plane. (Fig. $.) First draw the ground line X-Y (the ground 
line is always drawn as a horizontal line) and erect the indefinite 
perpendicular p-o-p'; now, since the distance of a point from 
the plane V is measured on H, lay off, from the ground line, a 
length o-p, equal to four inches— the distance of the given point 
from V— and the extremity, p, of this length represents the hori- 
zontal projection of the point. In like manner, to obtain the 
vertical projection of the point, lay off, from the ground line, a 
length o-f, equal to ten inches— the distance of the point from 



PROJECTION. 45 

the horizontal plane — and the extremity, p' } of this length repre- 
sents the vertical projection. 

The student should make it a point to clearly understand 
all points connected with the assumption and projection of a 
point before going farther, as a clear understanding of all subse- 
quent projections is dependent upon a clear conception of the 
projection of a point. 

Corollary. — From the foregoing it is obvious that the vertical 
projection of a point which lies in the horizontal plane is in the 
ground line, as the vertical projection of the point p, Fig. 5, is 
o t a point in X-Y ; also, that point f, in the vertical plane, is 
horizontally projected in (0) the ground line. 

70. The Projection of a Straight Line. — Plate No. 5. To 
obtain the projection of a straight line, it is necessary to project 
but two (any two) points of the line, and then join the projections 
with a straight line. Let M-N, Fig. 6, be a line in space; the 
two points projected are the two extremes of the line, M and N 
(this being the usual practice when dealing with a line of defi- 
nite length), M being horizontally projected at m, N horizon- 
tally projected at n, and m-n the horizontal projection of the 
line. It is obvious that m'-n' represents the vertical projection 
of the line. Fig. 7 represents the conventional projection of 
M-N. 

Corollary. — It is evident from the foregoing that the projection 
of curved lines is obtained in a similar manner, that is, by pro- 
jecting a number of points of the curves, and joining the pro- 
jections of these points by curved lines. 

71. The Projection of a Line which is Parallel to One of the 
Planes of Projection. — Plate No. 6. Let Fig. 1 represent the 
projection of a line M-N which is parallel to the horizontal plane 
of projection, m-n being its horizontal projection, and m'-n' its 
vertical projection. Since the line is parallel to H, all of its points 
are at the same distance from the horizontal plane, hence the 
vertical projection is parallel to the ground line — the distance from 
H being measured on V; also, since in the figure M-N-n-m 
M-m equals N-n, and the angles M-m-n and N-n-m are right 



46 MECHANICAL DRAWING. 

angles, the figure is a rectangle and M-N is parallel and equal to 
m-n. Therefore : 

A line which is parallel to one of the planes of projection has 
for its projection on that plane a parallel line of equal length, and 
for its other projection a line which is parallel to the ground 
line. (A line is projected in its" true length only on a parallel 
plane.) 

Fig. 2 is the conventional method of drawing the above pro- 
jection. 

72. To Find the True Length of a Line. — Plate No. 6. Having 
demonstrated that a line is projected in its true length on a parallel 
plane, it is obvious that, to show the true length of a line which 
is oblique to the planes V and H, it is necessary to revolve it 
about some point as an axis — usually one extreme if a definite 
line — until it becomes parallel to one of the planes of projection, 
when it will be projected on that plane in its true length. 

Let M-N, Fig. 4, represent a line in space which is oblique to 
both V and H, and let it be required to find the true length of 
the line by revolving it parallel to the vertical plane of projection. 
In the revolution, it must be understood, the position of all of 
the points of M-N are unaltered with respect to plane H; that is, 
if the point M, for example, be three inches from H in its original 
position, the point M must be three inches from H in the revolved 
position: the position of the line is altered with respect to V> 
only. Let the line be revolved, in accordance with the above, 
from the original position, M-N, about N as an axis, until it 
occupies a position M"-N, parallel to V, when its projections are 
m n -n on the horizontal plane (note that this projection is parallel 
to the ground line) and m n, -n' on the vertical plane of projection \ 
the line m n, -n' , then, represents the true length of M-N. 

The conventional procedure is illustrated by Fig. 3. The line 
M-N is assumed by its two projections m-n and m r -n' , the hori- 
zontal and vertical projections respectively. To find the true 
length by revolving into parallelism with the vertical plane, with 
the point n as a center and a radius n-m describe the arc m-m" \ 
now, since the distance of the point m is unchanged with reference 



PROJECTION. 



47 



PXATE No. 6 




48 MECHANICAL DRAWING. 

to the horizontal plane, the vertical projection of the arc m-m" 
is the straight line m'-m'", parallel to the ground line. The 
point n, being used as a center of revolution, remains fixed, hence 
its vertical projection remains unchanged and the vertical pro- 
jection of the revolved line is m ff '-n\ the true length of the 
line. 

73. The Projection of a Straight Line which is Perpendicular 
to one of the Planes of Projection. — Plate No. 6. Let M-N 9 
Fig. 5, represent a line in space which is perpendicular to the 
horizontal plane; it is obvious that all of its points are horizon- 
tally projected in the same point, and that the projection of 
the line on H is simply a point, while its vertical projection is 
a line m'-n f , perpendicular to the ground line; therefore, aline 
which is perpendicular to one of the planes of projection is 
projected on that plane as a point, while its other projection 
is a straight line perpendicular to the ground line; the conven- 
tional projection is shown in Fig. 6. 

74. The Assumption of Planes. — Plate No. 6. A point 
and a line are assumed by their two projections; a plane is assumed 
by its " traces." In Fig. 5 the triangle t-T-f represents a por- 
tion of a plane which is oblique to the planes of projection; the 
line t-T represents the intersection of the given plane — conven- 
tionally designated by the letter T, and called plane T — with 
plane H, and the line T-t' represents the intersection of T with V, 
These lines of intersection are called the " traces" of the plane. 
It is obvious that the traces of a given plane, as plane T, inter- 
sect in the ground line; also, that when the traces of a plane are 
once assumed, the position of the plane becomes fixed; hence a 
plane is assumed by its traces. 

Fig. 5 illustrates, also, the projection of a point P which is 
in the plane T, the projections p and ft being obtained by drop- 
ping perpendiculars to H and V respectively. 

Fig. 6 depicts the conventional method of assuming plane T, 
and the projection of point P in the plane. 

The student is advised to provide himself with two paste- 
board planes (one piece to be cut in the shape of a rhombus 



PROJECTION. 49 

and the other to be rectangular) to facilitate his conception of 
the following remarks : 

Fig. 8 is a drawing illustrating (i) a plane which is perpen- 
dicular to H and oblique to V, (2) a plane which is perpendicular 
to V and oblique to H, and (3) a plane which is perpendicular 
to both H and V. The student should note that the vertical 
trace of 1 is perpendicular to the ground line, G, that the hori- 
zontal trace of 2 is perpendicular to the ground line, and that 
both traces of 3 are perpendicular to the ground line. Fig. 7 is 
the conventional method of representing the above planes. 

In 3, Fig. 8, let P represent a point in the plane; also, let A-B 
represent a plane figure in the plane; it is obvious that all such 
points, lines, and figures within the plane are projected in the 
traces of the plane — the line a!-V ', for example, represents the 
vertical projection of the closed curve A-B. 

As a further exposition of the subject, and to demonstrate its 
practical use in mechanical drawing, the following representa- 
tive problems in projection are elucidated : 

75. Problem i. To Draw the Projections of a Hollow Cube 
when in Three Different Positions. — Plate No. 7. Let the first 
position be with all of its faces either parallel or perpendicular to 
the planes of projection, as 1, Fig. 1. Now, as a point is assumed 
by its two projections, so is an object assumed by its two pro- 
jections; hence, to assume the cube, draw 1, Fig. 3, which is the 
horizontal projection — the same as a plan of the cube, — then 
draw 2, the vertical projection — the same as an elevation — of 
the cube. The projections are drawn in this order, that the 
hole through the cube may be projected from 1 to 2, in which 
it is indicated by dashed lines. These two projections drawn, 
the object is assumed in its first position. 

For the second position of the cube, let it be assumed to be 
revolved, about a vertical axis through its center, through an 
angle of 45 , without altering its position with respect to the 
horizontal plane; that is, the cube does not move either up or 
down along the axis of revolution; 2, Fig. 1, illustrates this new 
position of the cube. 3, Fig. 3, represents the conventional 



5° 



MECHANICAL DRAWING. 



PLATE No. 7. 




PROJECTION. 51 

horizontal projection (plan) of the cube when revolved; to find 
its vertical projection, number all of the corners of the cube, 
when the problem becomes the projection of points, for, since 
the position of the cube remains unchanged with respect to the 
horizontal plane, the height of the projection of the various points 
on the vertical plane remains unchanged, and as the two pro- 
jections of a point are always in the same perpendicular to the 
ground line, the vertical projection of the points may be obtained 
by projecting horizontally from 2 and vertically from 3, when 
it is evident that the intersection of the projections from the like 
numbered point will be the new position of that point — its ver- 
tical projection. Having projected all of the points, join them by 
straight lines, and the vertical projection of the revolved cube is 
obtained. 

For the third position of the cube, let its position be altered 
with reference to the horizontal plane only; this is done by assum- 
ing the point numbered 8 to remain fixed, then revolving the 
object about this point through an angle of 30 . 3, Fig. 1, 
shows the cube when in this last position, and 5, Fig. 3, repre- 
sents its conventional vertical projection. To obtain the hori- 
zontal projection, since the position of the points are not changed 
with reference to V, and since the two projections of a point must 
lie in the same perpendicular to the ground line, project horizon- 
tally from 3 and vertically from 5, and the drawing numbered 6 — 
the horizontal projection of the cube when in its third portion — 
is obtained. 

Remarks. — Drawings 1 and 2, Fig. 3, are original projections; 
drawing 3 is a copy of drawing 1, turned through an angle of 45 ; 
4 is a projection; 5 is a copy of 4, tilted 30 ; and drawing 6 is a 
projection. 

76. Problem 2. To Draw the Projections of a Hexagonal Nut 
when in Two Different Positions. — Let the first position of the 
nut be when the plane of its base is parallel to the vertical plane 
of projection, as shown by position 1, Fig. 16. To draw the 
conventional projection of the nut when in this position, draw 1, 
Fig. 18, the vertical projection, or elevation, of the nut, then 



52 



MECHANICAL DRAWING. 



project 2, the horizontal projection, or plan, of the nut (the draw- 
ings are constructed in this order, that the corners of the hexagon 




may be projected from i to 2); these two drawings complete, 
the object is then assumed (by its projections) in its original 
position. 



PROJECTION. S3 

As a second position, let the position of the nut be changed 
with reference to the vertical plane only, by changing its position 
from the parallel one to one of 30 with the vertical plane, as 
shown by position 2, Fig. 16. To obtain the conventional pro- 
jection of the nut when in this position, draw 3, Fig. 18, its hori- 
zontal projection (which is a copy of 2, turned 30 to the ground 
line); then to draw its vertical projection proceed as follows: 

To find the projection of the outline of the nut, number all 
of the corners, that is, number every point of 1 and 2 (the same 
point having the same number in all of its projections) and trans- 
fer the numbering of 2 to 3, when, by projecting vertically from 
3 and horizontally from 1, the fourth position of the points is 
defined by the intersection of the projections from correspond- 
ingly numbered points; these points being then joined by straight 
lines give the vertical projection of the straight lines of the object. 
For the curved lines of the object, a number of points in each 
curve must be projected and their projections joined by curved 
lines. For example, take the curved edges of the front face of 
the nut; three points will be necessary, the two extremes and 
the middle point; this latter point is indicated by the figure 3 in 
Fig. 18, and the method of its projection shown. 

To project the circles showing on the front face of the nut, 
each circle should be divided into a number of points (twelve 
points, equally spaced, being a good working number), these 
points numbered, and then carried through the four drawings. 
(The point numbered 2 on the large circle, and the point num- 
bered 1 on the small circle illustrate the method of procedure.) 
To obtain that portion of the small circle showing at the rear of 
the nut — the position of the nut being such that the observer can 
see through it, — the projection of the points of the small circle 
in 1 are projected onto the rear of 2 (the line nearest the ground 
line), then copied on the rear of 3, and from there projected verti- 
cally to intersect with the horizontal projections from the same 
points of 1 ; the intersections are then connected by a curved line. 
Observe that the projections of the circles of 1 show as straight 
lines in 2 and 3, the straight -line projections being because the 



54 MECHANICAL DRAWING. 

plane of the circles is perpendicular to the horizontal plane; 
also note that, for a similar reason, two of the curved sides of 
the front face of the nut project in 4 as straight lines, the plane 
of each curve being perpendicular to V. 

77. Problem 3. — The Projection of a Small Hand-wheel. 
This projection is given to illustrate the application of the fore- 
going principles to ordinary mechanical drawing. Let the hand- 
wheel to be projected be such a one as is illustrated by Fig. 19. 
Now, suppose one has a front elevation of a machine drawn, in 
which the hand- wheel shows on the right side as the rectangle 
D-$-$-B (A, Fig. 20), at 45 to the horizontal, and is required 
to draw the right side elevation of the machine, necessitating the 
projecting of the hand-wheel to this hew position. 

To Project the Rim. — First, draw the full section of the 
wheel within the elevation — a sectional elevation — as is indicated 
by the dashed lines in A, Fig. 20, then on the front line of the 
elevation, D-5, as a center-line, lay out one-half of a "square 
view" of the wheel, as indicated by the dotted portion of the 
drawing. Next let the vertical center line, 5-5 (B), represent the 
position of the center line for the hand- wheel in the side eleva- 
tion drawing, and at some point along it — preferably some dis- 
tance above a horizontal line through the top point, 5, of A, or 
just below a horizontal line drawn through the bottom point, D t 
of A — cohstriict a similar drawing to the dotted portion of A; 
the projection may now be begun. 

In Fig. 20 the projected figure is but half complete, being 
ah amount sufficient to illustrate the method of procedure; the 
d6tted-half views are, however, all that is required to construct 
a finished projection. 

In such a projection as the one in hand it is best to consider 
but one "feature" of the object at a time, and to complete the 
projection of this one feature before taking up a second one, 
thus minimizing possible confusion. With this suggestion in 
mind, divide the hand- wheel into the hub, the rim, and the arms, 
and first consider the projection of the outside of the front face of 
the 1 rim— the straight line 5--D of the il 1 elevation, shown also as 



PROJECTION, 



55 



the dotted circle $-D of the same figure. To project this circle, 
first divide it into a number of points, as 5, 4, 3, 1, then project 




these points, perpendicularly, onto the straight line $-D, and 
number them that they may be easily followed. Next, locate the 



56 MECHANICAL DRAWING. 

outside circle of the dotted drawing of B y and divide ft into a 
number of arcs, equal to those of the same circle in A , and number 
each point to correspond with the same point in A. Since the 
projected view is at right angles with the original position of 
the wheel, it is evident that the extreme point 5 of A is the 
center point 5 of B, and that the center point 1 of A constitutes 
the two extremes of B, a fact which renders the numbering of 
the other points an easy matter. In the drawing, the circles are 
divided into a number of equal arcs corresponding to twelve 
equal divisions in a complete circumference: this is in accordance 
with the usual practice, which is to divide the circumference into 
an equal number of equal arcs, for when thus divided a circle 
presents duplicate divisions when viewed from first one position, 
and then from a position at right angles to the first one. With 
the points in each drawing properly numbered, project vertically 
from B and horizontally from A, and the intersection of the 
projections from the same numbered point will be the new posi- 
tion of that point; the points being then joined by a smooth 
curved line, give the side view of the outside of the front face of 
the rim. 

Next, consider the projection of the inside line of the front 
face of the rim — the dotted circles 9-8-7-6 — and proceeding by 
projecting a number of its points as explained above, the curve 
6-7-8-9, etc., of B is obtained — the side view of the inside of the 
front face of the rim. 

1 

The inside and outside lines of the front face of the hub of 
the wheel are projected in the same manner as directed for the 
lines of the rim. 

Now let the arrows s, s, s represent lines of sight directed 
against the front elevation A , the point of sight being at an infinite 
distance to the right, and having the figure well in mind, con- 
sider just what lines of the front elevation will be visible in the 
side view. Referring to the rim, it is evident that the outside 
and inside lines of its rear face will appear at top and bottom, 
respectively, in the side elevation, the method of projection being 
clearly shown in the drawing. It is also evident that the outside 



PROJECTION. 57 

line of the rear face of the hub will be partly visible in the side 
view. 

To Project the Arms. — From a previous explanation, it is 
evident that the center arm — that shown as a rectangle in A — 
will be shown as horizontal in B, extending to the extremes, 
right and left, and that the other two arms of A — the two extending 
to the extremes, top and bottom — will show on the vertical center 
line of B. First consider the upper arm of A, an inspection of 
which shows three points to project; .X, the intersection of the 
center line of its front face with the hub, and F, the intersection 
•of its side face with the hub. (Note the projection of these 
points from the dotted drawing of A to the front line of the 
sectional elevation of the arm.) By projecting horizontally from 
these points to an intersection with the vertical projection from the 
dotted position of the same points in B, three points are obtained 
— one central point and two extremes — through which the full- 
line curve Y-X-Y, representing the intersection of the arm with 
the hub, may be drawn, and the points F, F being established, 
the projection of the arm is completed by drawing vertically from 
these points to the inside line of the front face of the rim, the 
intersection of the arm with the rim being hidden. It is obvious 
that the curve of intersection, Y-X-Y, of the arm and hub is 
parallel to the same portion of the outside line of the hub. 

To project the horizontal arms of B, it is evident, from an 
inspection of the sectional elevation, that there are two sides or 
faces — the top and front — to project, the work being clearly 
shown by the drawing. 

It will have been observed that, because of the even number 
of arms in the hand-wheel, the drawings become symmetrical, 
and a number of the points project simultaneously. If the hand- 
wheel had an uneven number of arms, say five, the dotted half 
views would have to be complete views, and each arm projected 
separately, the circles being projected as explained. 

78. Problem 4. — Projections of a Frustum of a Hexagonal 
Right Pyramid and its Development. — Let the pyramid be 
assumed as resting on the horizontal plane, and let its position 



5* 



MECHANICAL DRAWING. 



with reference to the vertical plane be such as is defined by the 
drawings i and 2, Fig. 22 — its horizontal and vertical projection 
respectively. The pyramid is first assumed as a whole, the 

The Orthographic Projection of the frustum of a pyramid. 




Pyramid. 



Fig. 21. 



"frustum" not, as yet, entering into the problem. The draw- 
ings are constructed in the order numbered, that the edges of 2 
may be projected from 1. Now that the pyramid is fixed, let 




Fig. 22. 
the upper base of the frustum be formed by cutting the pyramid 
with a plane, T, which is perpendicular to V and at 30 with H, 
and let the cutting plane intersect the vertical center line of the 



PROJECTION. 59 

pyramid at a point one inch above its base. The plane of the 
upper base of the frustum is, of course, in the cutting plane, and 
this being perpendicular to V, the plane of the base is perpen- 
dicular to V, and is there projected as the straight line 7-10, one 
inch up the center line and at 30 with the horizontal, as shown in 
2. The frustum is now assumed, but the upper base shown only 
in its vertical projection. Now to obtain its horizontal projec- 
tion: 

The pyramid has six edges, and each edge has a point of 
intersection with the upper base; that is, to form the upper base, 
each edge has been cut by a plane. Now, each edge is shown 
in its two projections, and since the points of intersection of 
the edges with the plane of the upper base must be horizontally 
projected in some point on the horizontal projection of the edges, 
and since the projections of a point are always in the same perpen- 
dicular to the ground line, it is evident that the horizontal pro- 
jection of the points of intersection of the edges with the upper 
base is the intersection of the projection from the vertical inter- 
sections with the horizontal projection. For example, consider 
the point 12 of 2: 12 is on the edge 6-0; the horizontal projection 
of this edge is the line 6-0 of 1 ; the horizontal projection of the 
point must be on the line 6-0 (1) and must lie in the perpendicular 
through 12 (2) to the ground line; therefore the horizontal pro- 
jection of the point is the intersection of 6-0 (1) and the per- 
pendicular 12-12. The other five points of the upper base are 
projected from the vertical to the horizontal in a similar manner, 
and these points being joined by straight lines, as indicated in 
the drawing, represent the horizontal projection of the upper 
base. 

Let it be now required to show the true size of the upper 
base of the frustum. It is obvious that since the plane of this 
base is at an angle with H, the projected base in 1 does not repre- 
sent the true size of the base. To show the true size, the base 
must be projected onto a plane which is parallel to it. In draw- 
ing 4, let the line 7-10, parallel to 7-10 of 2, represent such a plane; 
the projection is then made on this plane, and to "show" it the 



<5o MECHANICAL DRAIV1NG. 

plane is revolved into the vertical plane of projection, the prac- 
tical solution being as follows: 

Draw the line 7-10 (4) parallel to and at an optional distance 
from the line 7-10 (2), then draw the indefinite perpendiculars 
7-7, 8-8, etc. It is obvious that the true length of the base is 
defined by the intersections of the perpendiculars 7-7 and 10-10 
with the line 7-10 (4). The true widths of the base are shown 
in its horizontal projection (1), for it is evident, since the plane 
of the base is perpendicular to V, a straight line joining the points 
8 and 12, for example, is parallel to H i and being parallel, will 
there be projected in its true length. Combining these "true 
widths" with the "true lengths" of drawing 4 — using the line 
7-10 as a center line — a drawing representing the true size of 
the upper base of the frustum is obtained. 

Let the frustum now be tilted on the point 4 of the lower 
base, until the plane of this base is in a position 30 with 
the horizontal plane, without changing its position with refer- 
ence to V f and let it be required to draw the H and V projec- 
tions. 

To draw the V projection, copy drawing 2, tilted to 30 with 
the ground line, as drawing 5, B. Now, since the position of 
the frustum with reference to V has not been changed, and since 
the two projections of a point must lie in the same perpendicular 
to G, the H projection is obtained by projecting horizontally 
from 1, A t and vertically from 5, B. This will give a complete 
projection — upper and lower base, and all edges; the drawing, 
however, shows a second method of projecting the upper base, 
by projecting the pyramid as a whole and locating the upper 
base by projecting the V intersections of the edges with this 
base to the horizontal projection of the edges — the same method 
as given for the first projection of this base. 

Development. — To develop means to unfold, and assuming 
the frustum to be hollow — made of sheets of pasteboard or metal — ■ 
let it be required to develop it. It is evident that in the develop- 
ment each base and every side will show in its true size and length. 
The true size of the two bases is known (the lower base being 



PROJECTION. 6 1 

in the horizontal plane, and projected in i in its true size), now 
to obtain the true length of each of the six sides : 

Since the pyramid is a right pyramid, all of its edges are of 
equal length; the drawing, however, shows the edges of unequal 
lengths: four of them, being oblique to both V and H, show a 
length less than the true length, and two, being parallel to V, 
show on that plane in their true length. The true width at the 
bottom of each face of the pyramid is known, this line being in 
the horizontal plane (i). To draw the development proceed 
as follows: 

With o (C) as a center, and a radius equal to the slant height 
of the pyramid — the true length of an edge — describe the indefinite 
arc 1-2-3, etc.; now use the line 0-4 as a center line, and from 
its intersection with the arc, with the true length of the base of a 
side of the pyramid as a unit, lay off (both above and below the 
center line) on the arc the lengths 4-3, 3-2, etc., and join these 
points with each other, and with the center, o; the resulting 
drawing will represent the development of the sides of the pyra- 
mid. To obtain the development of the sides of the frustum, 
find the true lengths of the various edges and transfer these 
lengths to drawing C. 

Let the frustum be cut — for development — along the edge 1-7; 
this edge being parallel to V (1) shows its true length on V; also, 
the edge 4-0 is there projected in its true length for the same 
reason; these lengths, then, may be taken directly from 2. To 
obtain the true length of the other four edges, each in turn must 
be revolved about o as a center (1), until parallel to V, when 
their true lengths will be there projected, showing in the drawing 
(2) as the lengths 4-9, 4-8, etc., on the slant height 4-0. These 
lengths are then laid off on the proper line of C, and the points 7, 
8, etc., thus obtained, when joined by straight lines, give the 
development of the line of intersection of the sides and upper 
base, completing the development of the sides of the frustum. 

In the development, the upper base should be attached to 
some point of the line of intersection of the sides with this base, 
and'the lower base should be attached to the line of intersection 



62 



MECHANICAL DRAWING. 



of the sides with the lower base. These two figures, 10 and 9, 
are copied from 4 and 3 respectively, and placed as shown (C) 
for balance. With C completed, if cut out along the full-line 
outline and folded together, it would give the object illustrated 
in Fig. 21. 

79. Problem 5. — Projections of a Frustum of a Right Cone of 
Revolution, and its Development. — Figs. 23 and 24. Let it be 
required to draw the projections of a frustum of a right cone of 
revolution, and to develop the frustum, the cone to be assumed 
and projected the same as the pyramid given in Problem 4. 



The Conev 



fig. 23 




This problem is solved by dividing the circle of the base of 
the cone into an equal number of equal arcs, and joining these 
points of division with the apex of the cone, thus giving a number 
of elements of the cone — working lines — which are projected 
through the several drawings in the manner described for the 
six edges of the pyramid, with the exception that, instead of 
joining the projected points with straight lines, curved lines are 
used. There are, however, two elements which cannot be thus 
projected, i.e., the center elements, C (V) and 4-C, 10-C (H); 
in locating the points through which the H projection of the 
curve of the upper base of the frustum is to be drawn, it is necessary 
to find the points X and Y — the projection of the intersection 
of the elements 4-C and 10-C with the plane of the upper base. 
To locate these points, since any section parallel to the plane 



PROJECTION. 



63 



of the lower base is a circle, if a plane X-Y be passed perpendicular 
to V and parallel to H, through point C, it is obvious that the 



PROJECTION No. 5, 







Name. 



Date. 



Fig. 24. 



The Orthographic Projection of the frustum of a cone. 



distance from the center of the cone to point C on the surface 
is equal to the radius C-X or C-Y of the circle cut by the plane 
X-Y; hence take the distance C-X or C-Y and lay it off on the 
line 4-C-10, as C-X and C-Y, which gives the required points. 

80. Problem 6. To Draw the Projections of the Intersection 
of Two Right Cylinders of Revolution, and to Develop the Cylin- 
ders. — Plate No. 8. Let the cylinders be assumed as shown by 
drawings 1 and 2, Fig. 5, and the first position of Fig. 1. 

To solve the problem, select a number of elements in each 
cylinder to use as working lines; with this in mind, pass a num- 
ber of planes, t-T-t', which are perpendicular to both V and H, 
cutting the smaller cylinder, S, in a number of elements, and since 
the two cylinders intersect at right angles, these same cutting- 
planes also cut elements of the large cylinder, L. These planes 
are passed through S, because all such planes intersect both 
cylinders . 

In drawing (Fig. 5), the method of procedure is to divide the 



64 MECHANICAL DRAWING. 

small circle (i) into an even number of equal arcs, and through 
these points of division to draw the vertical lines as shown. 

The first position of the cylinders is one in which the ele- 
ments of S are parallel to H and perpendicular to V, and the 
elements of L are parallel to V and perpendicular to H. Through- 
out the problem, L is assumed as resting on H. 

The view marked 4 presents a side view of 1, and is obtained 
by first constructing drawing 3, which is a copy of drawing 2, 
turned 90 , and then projecting vertically from 3 and horizontally 
from 1, and locating the intersection of the projections of the 
elements cut by the same plane. 

The view marked 6 is an angular, side view of 1, and is obtain- 
ed by first constructing 5, which is a copy of drawing 3, turned 30 
to the ground line, then projecting vertically from 5 and hori- 
zontally from 4. The location of the points P and P (6) require 
special mention. 

When looking against the vertical plane, as view 6 is taken, 
one cannot see that portion of the large cylinder beyond a section 
parallel to V through its center, in the drawing, beyond the 
extremes of the horizontal diameter through the point N (5). 
An inspection of the drawing shows no element-cutting plane 
through this point; to project this point, then, let an auxiliary 
element- cutting plane be passed through the point, and the pro- 
jection made in accordance with the drawing. 

Assuming the cylinders to be hollow and with open ends, let 
it be required to develop them, to roll them out flat, as shown by 

Fig- 3- 

The Development of the Small Cylinder. — Lay off the per- 
pendicular line 1- 1 (S, Fig. 4) equal to the true length of the 
small cylinder, and draw the indefinite horizontal lines 1-1. 
Now take the cord of arc 1-2 (1, Fig. 5), which is contained 
twelve times in the circumference of S, and lay it off twelve times 
on either of the horizontals 1-1, or the center line C-C, and through 
the twelve points thus obtained draw the twelve perpendiculars 
1-1, 2-2, 3-3, etc., completing the development of the small cylin- 
der. It is obvious that the greater the number of arcs in S 



PROJECTION. 



65 



PLATE No. 8. 



Li- 
O 



</> ' 




--]?__?-__-_ 

— Ht — I — v— " 
._jj_.l_Jtf.__, 

» — ff-+— f\ 



66 MECHANICAL DRAWING. 

(i, Fig. 5), the smaller the cord of the arc, and the more nearly 
accurate the development. 

In addition to developing S, let it be required to show the 
line of its intersection with L. There are already lines on the devel- 
opment representing the elements of S; also, drawing 4 shows 
these elements when parallel to V, and hence in their true length. 
The short method of showing the lines of intersection referred to 
is as follows: Working from the center line C-C of drawing 4 
(Fig. 5), take the lengths showing the horizontal distance of the 
various points of the intersection 1, 2, 3, etc., from this center 
line and transfer them to the development as the lengths C-i, 
C-2, C-?), etc., and draw the horizontal lines as shown, giving 
the points through which the curve representing the line of inter- 
section is drawn. 

To Develop the Large Cylinder. — Lay off the vertical length 
X (L y Fig. 4), draw two horizontal lines of indefinite lengths 
through its extremities, and draw the center line X-Y-X. Now, 
let the cylinder be cut along the element X (3, Fig. 5), and taking 
the lengths of the chords of the arcs, X-4, 4-3, 3-2, etc., until again 
coming to the point X, transfer them to the development as 
shown and erect the dotted perpendiculars, which represent 
those elements of L cut by the cutting planes and concerned in 
the intersection. In drawing 3, the elements of this cylinder 
are perpendicular to H and parallel to F, and hence are pro- 
jected on Fin their true length. The short method of showing 
the development of the intersection is as follows: Working with 
the line 4-4 (4, Fig. 5) as a center line, take the lengths repre- 
senting the perpendicular distances of the various points of the 
intersection 1, 2, 3, etc., from this center line and transfer them 
to the development as the lengths 4-1, 4-2, etc., and draw the 
horizontal lines as shown, giving the points of intersection through 
which the two ellipses, representing the holes. to receive the small 
cylinder, are drawn. 

With the two developments complete, if cut out along the 
full lines and rolled into cylinders, it will be found that the two 
can be fitted together the same as is illustrated by Fig. 1. 



PROJECTION. 67 

81. Problem 7. To Draw the Projections of the Intersection 
of a Right Cone of Revolution with a Right Cylinder of Revolu- 
tion, and to Develop Both. — Plate No. 9. Let the objects be 
assumed as by drawings 1 and 2, Fig. 5, and drawing i, Fig. 1. 
To solve the problem select a number of intersecting elements 
in each figure and project these elements as in the previous 
problem. 

To select the elements to be projected, pass a number of planes, 
t-i-T, t-2-T, etc. (Fig. 5), perpendicular to V and at various 
angles with H, through the apex of the cone and intersecting the 
cone and cylinder along elements, the practical method being to 
divide the circle of the base of the cone into an equal number of 
equal arcs, to project these divisions to the vertical projection 
of the base and then to join these points of division with the 
apex. These lines, then, represent the projections of the elements 
of the cone which are to be dealt with; the elements cut from the 
cylinder by the same intersecting planes are clearly shown by the 
drawing. 

To horizontally project the intersection of the two figures (the 
two ellipses shown in 2), project, vertically, from the points of 
intersection of the circle of the base of the cylinder with the 
different elements of the cone (1) to the horizontal projection 
of the elements of the cone — the radial lines of 2 — as in Problem 5. 
It is obvious that the small ellipse represents the visible portion 
of the horizontal projection of the intersection and the large 
ellipse the hidden portion; the case in hand is one of penetra- 
tion — the cone penetrating the cylinder. 

Drawing 3, Fig. 5, is a copy of drawing 2, turned 90 , and 
drawing 4 is obtained by projecting horizontally from 1 and 
vertically from 3, the lines of intersection being obtained by 
projecting horizontally from the intersection of the circle of the 
base of the cylinder with the different elements of the cone (1) 
to the various elements of the cone as shown in 4. The horizontal 
projection of the intersections (3) are obtained by projecting 
vertically from the points of intersection shown in 4 to the hori- 
zontal projections of the elements of the cone — the radial lines. 



68 



MECHANICAL DRAWING. 



PLATE No. 9. 



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PROJECTION. 69 

To Develop the Cylinder. — Drawings 1 and 4, Fig. 5, show an 
end and side view of the cylinder, respectively, the elements showing 
in their true lengths in the side view; to develop the cylinder, 
draw the vertical line L-L, Fig. 2, and draw the two indefinite 
horizontal lines L-L. Now, working from the circle of drawing i, 
Fig. 5, and assuming the cylinder to be cut along element L, take 
the length of the chord of the arc L-K and lay this length off on 
the development as the horizontal length L-K; next take the 
chord of the arc K-J and transfer it to the development in the 
manner shown, and so on, taking each chord in turn until again 
at the point L, when the length of the horizontal line L-L will be 
determined and is approximately equal to the distance around 
the cylinder — the circumference. It should be noted that the 
arcs H-X and P-Q are bisected, rendering the length of the 
development more nearly equal to the length of the circumference 
of the cylinder than if the chords of the above arcs had been used. 

Each point of division along the horizontals L-L represents 
the locus of an element of the cylinder, which, when connected 
by the perpendiculars L-L, K-K, etc., locate the elements required 
to find the development of the lines of intersection, the points oi 
intersection being found as follows: Take the true lengths of 
L-}, M-g, etc., from drawing 4, transfer them to the development 
as shown, and connect the points thus obtained with a curved 
line. - 

To Develop the Cone. — With o (Fig. 4) as a center and a 
radius b-i (1, Fig. 5) equal to the slant height of the cone 
(the true length of the elements), describe the indefinite arc 1-1. 
Now the base of the cone has been divided into twelve equal 
arcs, and since the length of the arc 1-1 must equal the length of 
the circumference of the base of the cone, take the chord of one 
of these arcs and step it off twelve times along the arc 1-1, 
then join these points of division with the center, o; this gives 
a drawing representing the development of the cone. 

To show the line of intersection of the cone with the cylinder, 
the true length of each element from the base or from the apex 
of the cone to its point of intersection with the cylinder must be 



7o 



MECHANICAL DRAWING. 



taken from either drawing i or 4 by horizontally projecting 
each point of intersection onto the slant height— a short method 
of revolving parallel to V— as in Problem 5, and transferred to 
the development as shown. 

82. Problem 8. To Find the Intersection of Two Right Cyl- 
inders of Revolution which Intersect at an Angle. — Fig. 25. This 
problem is met with in the drawing of pipe fittings, boilers, etc., 
wherever it is required to represent the intersection of two cylin- 
ders. 



2 3 4 



4 3 2 




Analysis. — Intersect the two cylinders with a system of planes, 
T, T, T } etc., which cut elements from both cylinders (as indi- 
cated by the ruled section) and find the intersection of the ele- 



PROJECTION. 



71 



ments of each cylinder cut by the same plane; these points, 
when joined by a curved line, represent the line of intersection 
of the cylinders. 

Solution. — Draw the semicircles M and JV and divide them 
into an equal number of equal arcs; through these points of divi- 
sion draw the lines 1-1, 2-2, etc., parallel to the elements of cylin- 
der A . From the points of intersection of these lines — elements — 
with the circle of the large cylinder, B (the plan drawing), project 
to the elevation to an intersection with the elevation of the same 
elements and join the points thus obtained, as shown. 

The developments are made as in Problem 6. 




83. Problem 9. To Construct a Conical Paper Shade for an 
Ordinary Incandescent Lamp. — Let the drawing for the pro- 
posed shade be that given in plan and elevation, Fig. 27. 

Analysis. — If the sides D-A and C-B of the shade be projected 
to an intersection at O, the shade becomes a cone, which, when 
developed and a proper allowance made for lap, may be cut from 
the paper and rolled into the required shade. 

Solution. — Produce the lines DA and C-B as suggested, and 
with the length O-A as a radius, and with O, Fig. 28, as a center, 
describe the indefinite arc B-B' . Now divide the circumference 
of the plan of the base of the cone into an equal number of equal 
arcs ; take the chord of one of these arcs and step it off along B-B f 
the same number of times it is contained in the circumference 
of the plan of the base; from the two extremes of the thus deter- 



72 



MECHANICAL DRAWING. 




Fig. 27. 




PROJECTION. 



73 



mined arc draw lines to the center 0. Now take a radius equal 
to O-D of the elevation drawing and describe the arc C-C, ter- 
minating in the radial lines from the center to the extremes of 
arc B-B f . To allow for lap, produce the arcs C-C and B-G as 
shown, and terminate them with a line parallel to C-B at the 
required distance; cut out along the heavy line outline (other 
lines being construction lines), fold up, and paste or pin the lap; 
that is, securely fasten the ends with C-B and C-B coincident, 
and the shade is finished. 

84. First and Third Quadrant Projections.— In mechanical 
drawing, it is often convenient to draw the plan of an object 
below the elevation — a procedure which is in strict accordance 
with the principles of projection, and a correct one in every way. 




El, 



3d 
Fig. 29. 



1st Quadrant 



~i_i — U 

Plan 

LT 

Fig. 30. 



Referring to Figs. 29 to 32, inclusive, Fig. 29 illustrates the first 
quadrant projection of an object, Fig. 30 representing the con- 
ventional projection. It will be noted that in this drawing the 
plan is below the elevation. Now assume the object to be trans- 
ferred to the third quadrant as in Fig. 32 and here (Fig. 31) the 
plan is above the elevation; hence- when the plan of an object 
is drawn above the elevation the object is assumed to be situ- 
ated in the third quadrant and the drawing said to be a third- 
angle drawing or projection; when the plan is drawn below 



74 



MECHANICAL DRAWING. 



the elevation, the drawing is a first- angle drawing or projec- 
tion. 



^ 



Plan 



G 



3d Quadrant 



El. 



Fig. 31 




85. Isometric Projection. — In the orthographic projections 
treated of thus far the objects projected have been so situated 
relative to the planes of projection as to project but one face of 
the object on each plane, and this is the usual practice. It is, 
however, often desirable to project two or more faces of an ob- 
ject onto one plane of projection that a general conception of 
the object may be obtained from the one projection or draw- 
ing. To construct a scenographic projection, which is obtained 
mechanically from and after the usual orthographic projections 
have been constructed, requires much time and labor, and because 
of the complicated arrangements occurring in machinery is prac- 
tically useless for such work. There is, however, a method of 
assuming objects to be so situated with respect to the planes V 
and H as to orthographically project two or more of its faces 
on each plane; such an arrangement may be called an "oblique" 
orthographic projection. 

There is a special case of oblique orthographic projection, 
called "isometric" projection, which portrays three faces of an 
object, is comparatively easy of construction, and is well adapted 
to the representation of fairly simple objects; particularly is it 



PROJECTION. 



75 



convenient and specially adapted to the representation of rect- 
angular objects or objects in which the principal lines are straight, 
parallel lines, as in the frame of a building. Having three faces to 
depict, there are three dimensions to be considered: (i) length, (2) 
breadth — both horizontal dimensions — and (3) height — a vertical 
dimension. 

Let it be required to construct an orthographic projection of 
a cube, the projection to show equal amounts of three adjacent 
faces: It is evident that to portray equal amounts of three 
adjacent faces of the cube it must be assumed to occupy a position 
relative to the plane of projection such that one of its diagonals 
will be perpendicular to the plane. Fig. 33 is a representation 




Fig. 33 



of the proposed arrangement. Having three faces projected, 
the projection on but one plane is all that is necessary to " tell the 
story." The vertical plane is the one adopted. Fig. 34 is a 
mechanical drawing of the arrangement, A being a side view 
of the cube and V-V a side view of plane V. It will be ob- 
served that the line 6-0 — a diagonal of the cube — is perpendicular 
to the plane of projection. The drawing marked B is a front 
view of the plane V-V, showing the orthographic projection of 



7 6 



MECHANICAL DRAWING. 



the cube when thus assumed, and is now called the " isometric " 
projection of the cube. 

It will have been noted in orthographic projection that a 
line is projected in its true length only when parallel to the plane 
cf projection. It is evident in the above case that the lines — 




Fig. 34 



edges — O-i, O-3, and O-4 make equal angles with the plane V~V f 
and making equal angles will be projected on that plane in equal 
lengths, which lengths, however, are somewhat less than the 
true lengths, being foreshortened (equally) in projection. The 
angle noted is an angle of 35°-i6', and the projected length is 
proportional to this inclination, being approximately equal to 
.8 of the true length. 

Referring to Fig. 34 again, and remembering that the three 
adjacent edges O-i, O-3, and O-4 of the cube form right angles, 
it will be noted that the projected angles between these lines are 
equal — equal to 120 . These three lines form the basis of opera- 
tion in isometric projection and drawing and are called the 
"coordinate axes." The perpendicular diagonal of the cube 
is called the isometric axis and the common point of intersec- 
tion, O, is called the origin. Fig. 35 is a representation of the 
coordinate axes, showing an optional notation for the three 
dimensions of isometric projection and drawing. 

There is a distinction between isometric "projection" and 
isometric "drawing," which can be illustrated by the case of 



PROJECTION. 



77 



the cube. Fig. 34, B, is an isometric "projection" of the cube, 
and, as has been explained, the length of the sides of the projec- 
tion are but .8 of the true length of an edge of the cube; in an 
isometric "drawing" it is customary to draw the lines represent- 



1-202_. 




Co-ordin ate Axes. 



Fig. 35. 



ing the edges of the cube of a length equal to the true length of 
an edge; as, for example, suppose one has a i-inch cube to 
project and to draw, the lines of the projection will be .8 inch 
long, while the lines of the drawing will be 1 inch long. 

To illustrate the application of the principles of isometric 
projection to practical draughting — the construction of isometric 
drawings — let it be required to construct an isometric drawing 
of an object the mechanical drawing of which is shown in A, 
Fig. 36. Having three faces to show, there are three dimensions: 
/ = length, b = breadth, and h = height. Now assume the object 
to be inclosed by a rectangular box, as is indicated by the dotted 
lines, the three dimensions of the box corresponding with the 
three extreme dimensions of the object — /, b, and h. 

Having such an assumption in mind, the isometric drawing 



78 MECHANICAL DRAWING. 

of the object may be begun, the first step of which (Fig. 36) is to 
draw the coordinate axes and assume one line to represent length, /, 
one to represent breadth, b, and one to represent height, h. The 
second step is to lay off on the co-ordinate axes /, b, and h lengths 
corresponding to /, b, and h of the mechanical drawing, after 
which complete the isometric drawing of the inclosing box by 
drawing lines from the extremities of these three lengths parallel 
to the co-ordinate axes, as shown. The third step of the draw- 
ing is to draw those lines visible in some one face of the box. In 
Fig. 36 this "one face" is the top face; in like manner the fourth 
and fifth steps are executed by drawing those lines visible in the 
front and right faces, respectively. The sixth step is to draw 
all other visible lines, and the seventh step to erase all construc- 
tion lines, giving a finished isometric drawing. 

To Dimension an Isometric Drawing. — Mechanical drawings 
are dimensioned in two directions, (1) horizontal and (2) vertical; 
in isometric drawing the dimensions are drawn parallel to the 
coordinate axes. An isometric drawing is rarely used for shop 
purposes, that is, as a working drawing having all dimensions 
given, etc., except for representing very simple rectangular objects, 
being most useful as a drawing for illustration and not for direc- 
tion or instruction. 

An isometric drawing intended for shop purposes should be 
completely and properly dimensioned and noted, eliminating all 
possible necessity for the workman to "scale" the drawing; how- 
ever, should it be required to scale an isometric drawing, the 
scaling must be done in the direction of the coordinate axes. 

Isometric Scales. — As has been described, the usual and 
practical method of constructing isometric drawings is to draw 
the lines of the drawing of the same, or some standard proportional 
length of the line of the object each represents, remembering that 
the " isometric dimensions" are measured in directions parallel with 
the direction of the coordinate axes; however, for some special 
reason one may have occasion to construct an isometric projection 
of an object. To construct such a drawing it is first necessary 
to construct an isometric scale — a scale on which all the dimen- 



PROJECTION. 



79 





m 


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\ V. 




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CO 

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So 



MECHANICAL DRAWING. 



sions are properly foreshortened, as i inch will be represented 
by a length .8 inch long. The scale is constructed by laying 
off the scale B, Fig. 37, the left side of which is graduated into 
full-length inches and subdivisions, then projecting horizontally 
to scale A, the right side of which is the foreshortened isometric 
scale. 




Fig. 37 



To use scale A for the construction of isometric projections, 
the object is measured with the left side of the scale — the full- 
length scale — and the projection constructed with the right side 
of the scale. 

By referring to Fig. 37 again it is seen that the full-length 
inches of A (those on the left) when projected horizontally to the 
fight side of B are 1.2 inches long; hence an isometric "drawing'* 
is 1.2 times the size of the object. , 

These isometric scales have no practical use and are given 
only as a matter of information in case one should ever wish to 
employ such a scale. 

86. Elementary Examples. — Let it be required to construct 
an isometric drawing of a cube each of whose faces contains a 



PROJECTION. 



81 



circle of the same diameter as the dimension of the cube. Let 
the drawing of the cube be constructed in accordance with the 
instructions already given (Fig. 38). Now. to draw the circle 
within the top face, A-B-C-O, since it will be tangent at the middle 
point of each side of the rhombus A-B-C-O, locate this point of 




each side, and with a center at B and a radius, R, equal to the 
distance from B to Y (the middle point of the opposite side of the 
rhombus) draw the arc Y-Y (the long one), then with the point 
O as a center, and with the same or equal radius, O-Y, describe 





A r - 





"B" 





Fig. 39. 



Fig. 40. 



the second long .arc Y-Y; next draw the diagonal C-A, and 
with the points X, X — the points in which this diagonal cuts 
the lines B-Y and O-Y — as centers, and a radius, S, equal to the 
distance from X to the points Y, Y, complete the ellipse Y-Y -Y-Y 
—the isometric drawing of the circle in the top face of the cube. 



82 MECHANICAL DRAWING. 

The ellipses of the right and left faces are drawn in like manner. 
This is the method of constructing all circles and circular arcs 
in isometric drawing, i.e., to first inclose the circle within a square, 
then to draw the square in isometric, then the circle as directed. 

Examples of simple isometric drawings are given in Figs. 39 
and 40, and in the various Plates. 



CHAPTER IV. 

DRAWING TOOLS AND MATERIALS. 

87. Introductory. — As all drawings consist of either straight 
or curved lines, entire or in combinations, and since in mechanical 
drawing these lines must be exact, the student in draughting 
must provide himself with a number of mechanical devices, 
technically termed ''instruments," calculated to facilitate his labor 
and precision. 

In draughting, as in all manual labor, the skill, natural or 
acquired, of the "operator" is a potent factor in securing results; 
however, in the selection of instruments this factor should be 
disregarded and the best instrument selected that can be afforded; 
for granted a skilled draughtsman may execute a fair drawing 
with inferior instruments, how much better work might he do 
with the very best; for the unskilled it is obvious the "very best" 
is none too good. The beginner should not think "anything will 
do to begin with," promising himself to provide an Ai outfit 
when he shall have acquired a fair degree of proficiency. Accuracy 
is one of the first requisites of a mechanical drawing and cannot 
be secured with poor tools. 

Having recognized the necessity of proper equipment, the ques- 
tion "What 'make' of instrument is the best" confronts the 
prospective purchaser. Of all of the numerous "makes" on 
the market, there may be said to be two general classes: (1) the 
instrument of triangular section and (2) the instrument of circular 
section. (See Figs. 48 and 49.) Consultation with experienced 
draughtsmen will elicit the information that there is a charac- 
teristic of instruments called the "feel" of the instrument, mean- 
ing the sensation produced on the nerves by the handling of the 
tool, one draughtsman preferring the first class of instrument 

83 



8 4 



MECHANICAL DRAWING. 



because of its "feel," its "touch" when in his hand, and another 
draughtsman preferring the second class of instrument for the 
same reason, it being simply a case, of what the man is accus- 
tomed to. 

The selection of instruments, then, becomes a question as 
to details of construction, and is a matter of finance and choice with 
the buyer, he being "safe" in purchasing a good quality of any 
of the standard maizes. 



fev-.:-;.l 



.'■.'•,\..*..",-,iy., .•{■■■•''■■. •••■•• . . . \ 




Fig. 41. 

I. Compass with pencil -leg and needle-point. 2. Hair-spring dividers. 
3. Lengthening-bar. 4. Pen-leg. 5, 6. Ruling-pens. 7. Lead-box. 8. Bow- 
pencil. 9. Bow dividers. 10. Bow pen. 

"Just what tools are necessary, what to buy," is the next 
question, and is one of much latitude, since there are tools and 
devices to be had by the score. As in every question, there are 



DRAWING TOOLS AND MATERIALS. 85 

two sides to be considered: (1) what can one get along with, and 
(2) what ought one to have?; the answer to the first being 
instruments for drawing straight and curved lines, representing few 
tools and a minimum outlay, while for the second question it might 
be said that many tools were desirable, representing a maximum out- 
lay. Of these two extremes a mean is taken, and the following list 
names the articles that should comprise a good, practical " outfit ": 
I. A case of instruments, to consist of 

2 ruling-pens, 1 large, 1 small. 

1 compass, with pen and pencil-legs and extension-bar.. . 
1 pair dividers, with hair-spring adjustment. 

3 bow instruments: (1) pen, (2) pencil, and (3) dividers. 
1 box leads, hard and medium grades. 

2. Drawing-board. 

3. T square. 

4. 2 Triangles: (1) 45 and (2) 3o°-6b°. 

5. Irregular curve. 

6. Architect's scale. 

7. Thumb-tacks. 

8. Pencil, hard lead— HHHHHH. 

9. Pen and penholder. 

10. Erasers — pencil and ink. 
n. Ink, black. 

12. Rag for cleaning instruments. 

13. Blotter. 

14. Soapstone pencil. 

The instruments named under item 1 can be secured sepa- 
rately; the "trade," however, provides a neat and convenient case 
(Fig. 41) for the tools, and as the additional cost of the case is 
small when compared with the cost of new instruments, it is ad- 
visable to purchase a case; the tools will then have a proper recep- 
tacle, and with ordinary care this will minimize the necessity 
of purchasing new tools. 

88. The Ruling-pen. — Since the major portion of most draw- 
ings is composed of straight lines, the ruling- pen easily becomes 
the instrument of prime importance. The first requisite of a 



S6 



MECHANICAL DRAWING. 



4^ 






good ruling-pen is that the temper shall be just right; it must 
not be too soft, rendering frequent sharpening necessary; neither 
must it be hardened to a degree rendering it brittle and susceptible 
to fracture. The "temper" is a quality which cannot be recog- 
nized by the eye alone because of the high polish given the tool; 
the instrument must be given a trial and if not of the proper degree 
©f hardness it may, provided the stock be right, be retempered. 
Apropos of further discussion, let the student acquaint himself 
with the names of the various parts of the ordinary instrument 
<Fig. 42). 

The handle is usually of bone, wood, or metal, and 
can be homogeneous with the nibs, or separate and 
fastened thereto, as is usually the case, in the which 
the handle should always have a firm and secure fit, 
as any slight looseness will tend to render the work of 
the pen inaccurate. 

The nibs are the "pen," and in the ordinary instru- 
ment are fashioned with a tendency to spring apart, 
a tendency for the pen to remain "open"; that they 
may be brought together, the thumb- screw is em- 
ployed, only one nib being threaded, the other having 
a smooth-bored hole. 

The thumb-screw. should have a knurled head (the 
edge cut into small points) that it may be easily oper- 
ated, and its shank should be threaded to the head, or 
otherwise so fashioned that when in position it is 
capable of bringing the nibs exactly together. The 
thread of the screw should never be allowed to become 
corroded, but should be frequently oiled with gun or 
bicycle- oil. The fit of the screw in the nibs should 
be snug and even; there should be no "binds" or 
"play." 

The "business end" of the pen, for ordinary work, 
should be slightly rounded as A, Fig. 43, not like B; 
the nibs should be exactly of the same length, ground 
to a knife-edge — not a point — and free from "burrs" inside and 









to 
_Q 

H 



Fig. 42. 



DRAWING TOOLS AND MATERIALS. 87 

out. A new pen is usually ready for use, and the student will do 
well to carefully note the shape and sharpen of it. 






Fig. 43. 

A pen '-in condition" and properly handled should rule a 
smooth and even line (1, Fig. 44) of uniform width and with clean- 
cut sides; also, the pen should produce lines varying in thickness 
from a light "hair" line to a heavy line of one-sixteenth of one 
inch, or greater, in width. Since the best pens cannot for a great 
while, in use, maintain an edge sufficiently fine to produce the 
hair line, it is well, having two pens, to reserve the small pen for 
light lines and the larger pen for heavy lines. 

A pen "out of condition" will rule, if at all, rough, ragged* 
and intermittent lines. Some of the common causes for such 
results are: one nib may be longer than the other, the pen may 

1 



2. 

A.* 
5.' 



Fig. 44. 

be too pointed, there may be burrs or rough places on the points,, 
and above all the pen may not be held properly. In testing a 
pen, a ruling edge should always be employed. 

When a pen produces a line like 2 or 3, Fig. 44, one of the 
nibs will be found to be longer than the other; a line like 4 indicates 
that the pen-points are not smooth — a small nick may be broken 



88 MECHANICAL DRAWING. 

out. These are usually the troublesome features encountered 
when only heavy- and medium weight lines are desired; the hair 
line is more difficult to draw and lequires the clever manipula- 
tion of a pen in the best condition. To rule very fine lines the 
pen must be sharpened to a nicety; a line like 5 is the product of 
a dull pen, and is the result of attempting a finer line than the 
pen, as sharpened, will rule. When such results are obtained, 
let the draughtsman stand with his back to the light, and holding 
the pen lengthwise and in line with the eye, look directly onto 
the points of the pen — the points of the nibs — and he will observe 
two " bright spots"; the finest line that can be ruled with the 
pen is a line whose width is the sum of the widths of the two 
bright spots, and the pen being closed, the ink must flow by con- 
vection around the points and not through or between them as 
it should, and the flow being irregular, produces a line as shown. 

The lines depicted in 4 and 5 may also be caused by a dirty 
pen; ink may have been allowed to dry on the points; a thorough 
cleaning is the remedy. No. 5 may also result from undue pres- 
sure on the pen in the ruling. In ruling fine lines the pen should 
be well cleaned after every charge of ink has become exhausted. 

When a pen is "out of condition," the remedy is to regrind 
it — sharpen it. The manufacturers of instruments maintain a de- 
partment for the sharpening of pens, repairs, etc., but should one 
send his pen to the factory every time it needed regrinding, he 
would justly forfeit his title of " Practical Draughtsman. " Every 
draughtsman should be able to keep his instrument in first-class 
condition, for while there are some general instructions which 
may be given for the proper handling of the pen, draughting is 
like writing; no two men will hold the pen in exactly the same 
position, and the pen must be sharpened to suit the user. 

To sharpen a pen, close the nibs until they have contact, 
and with a fine-grained oil-stone at hand, round off the points 
until they are even and in shape, comparing with A, Fig. 43, 
not B. Now note the bright spots; these must be ground away, 
the pen must be really sharpened — the same as a knife-blade — 
not pointed. To do this, open the nibs, and taking them one 



DRAWING TOOLS AND MATERIALS. 



89 



at a time, consider it as a chisel or knife-blade to be sharpened 
on but one side — the outside — and by moving it back and forth, 
turning it slightly from side to side, grind the points until no 
bright spots are visible. Great care must be exercised in the 
operation, else the point at which the "spots" disappear be 
passed and the nibs become of uneven lengths, necessitating 
another trial of the entire operation. A careful procedure should 
produce a pair of nibs of even length, truly and smoothly shaped 
and sharpened on all sides; should any burrs occur, however, a. a 
point that cannot be treated with an oil-stone or oil-slip, they 
may be removed by the use of very fine emery-cloth. 

To try the pen, secure a piece of drawing paper and a straight- 
edge, and having thoroughly wiped all oil and dirt from the nibs, 
screw them together until about T V' to ^ n apart, and charge the 
pen with ink in such quantity as will fill it for about one-quarter of 
an inch from the point (Fig. 45). (To charge the pen, take the tool 
in the left hand, if right-handed, and taking the stopper from 





Fig. 45, 



Fig. 46. 



the ink-bottle in the right hand, insert the point of the quill between 
the nibs, when the ink will run into the pen.) The pen being 
charged, transfer it to the right hand and manipulate the straight- 
edge with the left hand; hold the pen with the thumb-screw on 
the outside — away from the hand — and in such a position that 
the screw may be operated by the thumb and second finger, and 
holding the pen perpendicularly, place it against the ruling- edge 
as in Figs. 45 and 46. It will be noted that in this position the 
curvature of the instrument throws the pen point well away from 



9° MECHANICAL DRAWING. 

the straight edge (this is important); also that the nibs are parallel 
to the ruling edge; maintaining this position, move the pen 
along the ruler, drawing from the body, with just sufficient down- 
ward pressure to secure smooth and even contact with the paper 
and a pressure against the straight-edge sufficient to maintain 
the guide. Varying the weight of line by increasing or decreas- 
ing the width between the nibs by means of the thumb-screw 
operated by the thumb and second finger, rule a number of lines 
and note their contour. Should any of the before-mentioned 
" faulty" lines result, the cause can be recognized and the fault 
eradicated. 

In the trial for the very fine lines, much care should be exer- 
cised not to screw the nibs so tightly together as to cause them 
to "flare" out at the point, as in Fig. 47. 

With the pen in first-class condition, the ruling 
of lines becomes a matter of practice. Much care 
must be exercised to maintain the original position 
of the pen — that depicted in Figs. 45 and 46 — when 
drawing it along the guide, for should it be changed 
by throwing the handle out and the point in and 

,-, against the guide, the ink will be drawn under the 

Fig. 47. & b ' 

guide and cause a blot ; the small space between the 
straight-edge and the pen-point must be maintained. Furthermore, 
should the position of the pen be altered in any way changing 
the original space between the point and the guide, the line will 
not be a right line — all of its points will not lie in the same direc- 
tion — and as mechanical drawing is an exact art, it is obvious 
such lines will not answer. 

Blotting will be the first trouble experienced by the beginner, 
and will tend to augment the inaccuracy of his lines; in trying to 
secure sufficient space between the pen-point and the ruling-edge 
he will assume a position, to begin with, other than in a perpen- 
dicular, and as the ruling proceeds and the hand gets farther 
from the body, the tendency will be to "straighten " up the pen. 

While a perpendicular position of the pen is recommended, 
good results may also be obtained by slightly leaning the pen in 




DRAWING TOOLS AND MATERIALS. 



91 



Joint 



the direction of the line, keeping it, however, in a vertical plane 
parallel with the straight-edge. 

89. The Compass. — Fig. 48. The compass — an instrument 
for drawing circles — is next to the ruling-pen in importance, and 
consists of five pieces: (1) the com- 
pass proper, (2) the pen-leg, (3) the 
pencil-leg, (4) the extension-bar, 
and (5) the center-point. 

All the joints in the instrument 
should have a firm, even bearing, 
and should be free from all binds 
and play. In purchasing a new 
instrument, all the parts should be 
placed together, the joints inspected, 
and the fits noted. With the pen- leg 
in position, the instrument should 
be closed and the center-point set 
with its point slightly in advance 
of the pen-point; if the center- 
point be fashioned with a shoulder, 
this should come flush with the pen- 
point. When the center-point is 
once set for the pen, it should never 
be changed; the pencil-point must 
always be adjusted to the center- 
point. . 

The remarks on the ruling-pen 
apply also to the pen of the pen-leg; 
the pencil-point will be treated of in 
the discussion of lead-pencils and 
leads. Needle P° int 

The accuracy of the construction jr IG 

of the tool may be remarked by 

closing the instrument and noting the position of the points, 
which should lie in a plane perpendicular to the axis of the head 
and passing through the center of each leg, or should the instru- 



Socket Jc 



Joints/ 



T. screw 1 




screw 



9 2 MECHANICAL DRAWING. 

ment be broken at the knees (to the same degree) and the points 
brought together, they should coincide. 

To use the compass, the points should be brought to the 
proper adjustment and the instrument broken at the knees — 
each knee to the same degree — until the legs of the tool are par- 
allel; now place the center-point on the point about which the 
circle is to be drawn and press it "home" if the point is " shoulder" 
fashioned, otherwise give it only such pressure as to cause the 
point to prick the paper to a depth sufficient to fix it. Do not 
punch large holes in the paper or the work will be inaccurate 
and the paper unsightly. 

With the center-point fixed, erect the instrument to a position 
such that a line dropped from the center of the head will be per- 
pendicular to the plane of the paper, and if the adjustment be 
correct, it should pierce the plane of the paper at a point bisect- 
ing a line joining the two points of the compass. From this first 
position, slightly incline the instrument in the direction in which 
it is desired to draw the circle — usually clockwise, from left to 
right — and with a downward pressure, only sufficient to maintain 
the center-point where fixed and to secure a light contact between 
the paper and the ruling-point, turn the instrument in the direc- 
tion of its inclination until the circle is described; should any part 
of the line be dim or incomplete, go over it again in the same 
manner until the line is clean-cut; never reverse the order and 
run "backwards" over the line. 

The compass should be used only for the larger-sized circles, 
those of small diameter being drawn with the bow-pen or bow- 
pencil. When a circle of greater diameter than the instrument 
just described will "span" is to be drawn the extension-bar 
must be used. To use the bar, remove the ruling-point and insert 
the shank of the bar in the socket of the compass-leg vacated by 
the shank of the pen-leg, and the latter shank in the socket of the 
extension-bar, and secure all joints; next break the knees of 
the instrument until the two legs are parallel, then pro- 
ceed as above described. With the extension-bar in use, a line 
through the head of the tool and perpendicular to the plane of 



DRAWING TOOLS AND MATERIALS. 



93 



loint. 




a 



o 



the paper will pierce the paper at a point nearer the center-point 
than the ruling- point, in which case it is well to steady the long 
leg with the free hand; when possible, however, it should be a 
" one-hand ' ' operation. 

The compass is a very delicate instrument and to preserve its 
accuracy should be very carefully handled and cared 
for. 

90. The Dividers. — Fig. 49. The dividers are 
used to lay off divisions and to transfer distances 
from one point to another, as in copying drawings, 
and should be provided with a hair- spring adjust- 
ment for very fine work. This instrument is even 
more delicate than the compass, the legs being 
tapered to needle-points, and should be very care- 
fully handled, else the points be destroyed and the 
accuracy of the tool impaired. Should one or both 
of the points become broken or blunted, they can 
be repointed by grinding on an oil-stone. 

To test the accuracy of the instrument, close the 
tool, when the legs should be of equal length and 
the points exactly in line and in a plane perpendicu- 
lar to the axis of the head and passing through the 
center of each leg. 

To use the dividers, say to lay off a given line 
from a given point, hold the instrument near the 
top with the thumb and first finger and insert the 
second and third fingers between the legs of the tool. 
With the instrument thus in hand it can be opened 
and closed with the one hand. Now set one leg with 
its point at one extreme of the line and open the 
dividers to a width closely approximating the length 
of the given line, then bring the width between the 
points to exactly equal the length of the line by ad- 
justing the hair-spring; next transfer the tool to the 
given point and place one point exactly on it; then, with the 
Other leg in the desired position, bring its point in contact with 



94 



MECHANICAL DRAWING. 



the paper and either mark the point with a pencil or raise the in- 
strument, with the point fixed, until the leg is perpendicular to 
the plane of the paper, then slightly prick the surface. In no 
case should the prick-marks puncture the paper, as it renders the 
paper unsightly and the work inaccurate. 

The dividers are to be used where the work is comparatively 
large and the lengths variable. The joint at the head should be 
quite firm, smooth, and even, and free from all binds and play. 

91. The Bow-pen. — Fig. 50. The bow-pen is a small com- 
pass with the pen-leg only, the joint at the head is done away with, 

and the tool so fashioned that the 
legs tend to spring apart. The es- 
sentials of a good bow-pen are: the 
temper of the pen-point should be 
that necessary in a good ruling-pen, 
the spring of the instrument should 
be quite stiff, the threaded member 
should be smoothly and truly cut, 
and the thumb-screw should be 
capable of bringing the points ex- 
actly together. 

To adjust the instrument, it 
should be closed by means of the 
thumb-screw and the center-point 
set slightly in advance of the pen- 
point, when, if the instrument be 
well and accurately made, the points 
will lie in line with each other and 
in a plane passing through the center of each leg. 

To facilitate the use of the instrument and to minimize the 
" wear and tear, " instead of opening and closing the tool by means 
of the thumb- screw, it is well to proceed as follows: To close the 
pen, hold it between the thumb and the first finger of the right 
hand, press the legs together by means of the left hand, and with 
the second finger of the right hand turn the knurled nut to the 
proper position. To open the instrument, hold it as for closing, 



^Adjusting 
\ screw 



Nibs 




Fig. 50. 



DRAWING TOOLS AND MATERIALS. 



95 



and with the left hand "stay" the legs, and operate the nut with 
the thumb of the right hand; when the nut is approximately at 
the desired position, permit the legs to spread gently until the 
nut prevents further movement. This operation requires much 
caution to prevent the legs from slipping from the grasp of the left 
hand and violently springing against the nut, an accident several 
of which might spoil the threaded members of the tool and render 
it unfit for use. 

The remarks on sharpening the ruling-pen are applicable to 
the sharpening of the bow-pen; as a special caution, however, it 
may be added the center-point should be removed during the 
operation. 




Adjusting 
screw 



^Needle point Lead 
Fig. 51. 




Adjusting- 
screw^/ 



Fig. 52. 



The bow-pen should always be used on small work, and in 
fact wherever possible, as it is easier of manipulation than the 
compass. 

92. The Bow-pencil. — Fig. 51. The bow-pencil is a small 
compass with the pencil-leg only, and is covered by the remarks 



9 6 MECHANICAL DRAWING. 

on the bow-pen, the method of manipulation, adjustment, etc., 
being the same for both tools. 

93. The Bow-dividers.— Fig. 52. The bow-dividers are small 
dividers and are used in the same manner as the other two bow 
instruments. Other specific points are covered by the remarks 
on the large dividers. 

The bow-dividers are used for small work or wherever possible, 
as the tool has the advantage over the larger instrument in that 
it is not liable to variation when once set. The principal use of 
the tool is for the laying off of a large number of equal divisions. 

94. The Box for Leads. — Fig. 41. The box for leads should 
contain leads of various degrees of hardness and of a shape and 
size to fit the instruments. 

95. The Care of Instruments. — Draughting instruments are 
instruments of precision and should be carefully handled and 
cared for. When through with a tool, it should be carefully 
cleaned with an old linen or cotton rag or chamois-skin, then at 
once placed in the case. Ink or other foreign substances should 
never be allowed to dry on the tools. After considerable hand- 
ling, even with the best of care, a slight corrosion will make its 
appearance, particularly on the ruling-pen; this is due to con- 
tact with the moisture of the hands and cannot be eliminated, 
save to a degree. 

96. Drawing-boards. — The trade has a large variety of 
drawing-boards, adjustable tables, etc., on the market; it is well, 
however, for the beginner to first provide himself with some 
simply constructed board, such as is shown in Fig. 53. The 
stock should be of well- seasoned, clear, soft pine, such as is used 
for pattern-making; the warping tendencies of the material should 
be minimized by saw-cuts on the back and with cleats well secured 
to the board. The top face should be given a smooth, even. 
finish and one end face trued and jointed to this face. The 
planed surface is the " working -face " and the jointed edge is 
the " working-edge." With the working-edge at the left hand 
and the working-face up, the edge farthest from the observer is 
the top of the board and that edge nearest him the bottom. The 



DRAWING TOOLS AND MATERIALS. 



97 



student should fix these features of the board in mind, as they 
will be used in further discussions. 

97. The T-Square. — The T-square is a device used as the 
basis of construction for all accurate drawing, and derives its 
name from its shape and use, being fashioned like the letter T, 
and used as and like a square. Fig. 53 illustrates the ordinary 
T-square, the short piece being the "head" of the square and 
the long piece the "blade." 




Fig. 53. 

T-squares are made of various materials, the more common 
of which are wood, rubber, amber, and metal, and with solid 
and adjustable heads and various attachments. A good work- 
ing-square, one answering all practical purposes, is made of 
straight-grained hard wood, with adjustable head and a blade 
with amber edges. The advantages possessed by such a square 
are its greater range of usefulness because of the adjustable head, 
which renders it more than a simple square, and the advantage 
of a transparent edge. For very fine work a metal square is 
the best, being free from warping tendencies and capable of 
maintaining the most accurate straight edge, while its greater 
weight makes it the most stable, and with ordinary care slippage 
is eliminated. The objections to the metal square are its exces- 
sive first cost and susceptibility to corrosion. 



98 MECHANICAL DRAWING. 

In purchasing a T-square, the size of the drawings to be made 
should be considered and a square selected which has a blade 
of even length with the board required for the work. The work- 
ing-edge of the head should be a true plane surface, jointed with 
the top face; the blade should be planed true on all sides and the 
faces jointed. 

The T-square is used to square the paper on the drawing- 
board, and as a guide for the ruling-points for drawing horizontal 
lines, and for the triangles. To use the square, place it on the 
board and bring the working- edge of the head against the work- 
ing-edge of the board, then draw along the working-edge of the 
blade with pen or pencil. The square should be operated with 
the left hand and the drawing done with the right hand, if right- 
handed. The head of the square should be held near the center 
in a firm though not a strained grasp, and having drawn a line, the 
square may be shifted up or down and any number of parallel 
lines drawn. In shifting the square, much care should be exercised 
to grasp the head at the same point and with uniform force, 
else the lines will not be parallel. 

The blade of the square should be preserved as a ruling-edge 
and never used as a guide for a knife or other edged tool when 
cutting paper; if limited for straight edges, one edge only (the 
upper) may be reserved as a ruling- edge and the other edge used 
as a "cutting-edge." Should the ruling-edge become untrue, if 
the square be a wooden one, it is an easy matter to remove and 
true it by planing. 

98. Triangles. — Fig. 53. Having provided for the accurate 
ruling of horizontal lines with the T-square, it is then necessary 
to provide means for drawing perpendicular and angular lines, 
an end secured by the use of triangles. 

Triangles of various sizes and angles may be had of wood, 
rubber, amber, metal, and a number of other materials, of which 
the triangle made of amber is the most desirable because of its 
transparency and cleanliness. The objection to the amber 
triangle is its susceptibility to heat, an exposure of some time 
to the sun's rays often causing the triangle to warp; however, 



DRAWING TOOLS AND MATERIALS. 99 

should such a triangle become warped, it may be straightened 
by reversing it and again exposing it to the sun. The objection 
cited is not of great moment, as there is no good excuse for leaving 
one's triangle thus exposed. 

As to the size of a triangle, it should be of ample dimensions 
for the work in hand; one engaged in constructing large drawings 
should have a large sized triangle, while for small work the smaller 
sizes are more convenient. 

The angle of a triangle is a much discussed subject, though 
draughtsmen unite in recognizing the desirability, almost neces- 
sity, of being provided with angles of 90 , 45 , 30 , and 6o°. 
The manufacturer meets this requirement with two triangles: 
one called the 45 triangle, which has one angle of 90 and two 
angles of 45 , and a second one called the 3o°-6o° triangle, or 
simply the 6o° triangle, which has an angle of 90 , one of 6o°, 
and one of 30 ; with these two triangles and the T-square, a 
circle may be divided into twenty- four equal parts, which gives 
a division every fifteen degrees. 

That a drawing may be exact, it is necessary that the triangles 
be absolutely true. To test a triangle for the 90 angle, place it 
against the working-edge of the T-square, with the right angle up 
and draw through a given point a vertical line; now reverse the 
triangle — turn it over from left to right or vice versa — and through 
the same point draw a second vertical line; if the two lines coin- 
cide, the angle is correct, otherwise the inaccuracy will show as 
diverging lines, becoming more and more apparent as the lines 
recede from the point. The test of the triangle may be made by 
any other angle by first drawing a circle, then with the angle 
against the working-edge of the T-square draw a line through 
the center of the circle and intersecting the circumference; now 
reverse the triangle and draw a second line through the center of 
the circle intersecting the circumference. If the triangle is true, a 
horizontal line through one of the points of intersection on the 
circumference will pass through the other point. 

Should the edges of a triangle become nicked or otherwise 
injured, or should the angles be untrue, the triangle is practically 



ioo MECHANICAL DRAWING. 

useless and should be discarded, though a skilled workman may 
eliminate the faults by planing. 

It has been noted that the T-square should be used for all 
horizontal lines; the T-square and triangles should be used for 
all perpendicular lines and all other lines of known angles. 'The 
triangles should never be used " free-hand" (without the T- 
square), as such a procedure is time-consuming and inaccurate. 
As a last word, it may be added, never use a triangle as a guide 
for a knife-edge in cutting. 

99. Irregular Curves. — Fig. 72. Irregular curves are devices 
used as a guide for drawing all arcs other than the arcs of circles. 
They are made of various materials, shapes, and sizes. In pur- 
chasing a curve, one adapted to the work in hand should be 
selected, as curves to fit all usual figures are to be had. The 
best curve, like the triangles, is one made of amber. 

The manner of using the curve is set forth in Sect. 197, and 
requires much practice to attain proficiency. 

100. The Architect's Scale. — As all mechanical drawings are 
drawn proportional to the object, it is necessary to "lay off" 
the drawing to scale. Scales for this purpose may be had of 
various materials,, principal among which are ivory, boxwood, 
and metal, and graduated to any denomination. There are two 
denominations in general use, (1) a graduation of tenths of an 
inch, and (2) a graduation of sixteenths of an inch. A scale 
graduated in tenths inches is called the "Engineer's Scale," and 
the scale with T Y" divisions is called the "Architect's Scale." 

The engineer's scale is used mostly in government work, 
mapping, surveys, etc., while the architect's scale is the one of 
general usage, the common scale being of boxwood and known 
as the "architect's tringular scale," the word "triangular" signify- 
ing three- sided (Fig. 54). 

The ordinary architect's scale contains eleven separate scales: 
(1) A full-sized scale which is 1 foot in length, the foot is gradu- 
ated into inches, and the inches into sixteenths inches. This 
scale is designated by the figure 16 under the 6-inch division 
of the scale, or in some cases at one end of the scale. In using 



DRAWING TOOLS AND MATERIALS. 101 

this scale, the drawing is laid off inch for inch of the object drawn. 
The next scale for drawings is a scale of three-fourths size, or 
g" = i r . To construct a drawing to this scale, the dimensions 
are reduced mentally, or otherwise, to three- fourths of the original 
and the drawing laid out with the full-size scale. Half- sized draw- 
ings, or a scale of 6" = i', which is the next usual scale for draw- 




Fig. 54. 

ings, are constructed in a similar manner. Should it become 
necessary to lay off a division smaller than T y, say -3V or ^", 
this may be done by using the full- sized scale and bisecting the 
T V' division with the eye for thirty seconds and quartering the 
T V' division for sixty-fourths; with a little practice very accurate 
divisions may be made. 

(2) The next scale is a scale of one- fourth size, or 3 ,, = i / . 
This scale is found on the "flat" of the tool adjacent to the full- 
sized scale, on the zero end, and is designated by the figure 3 
stamped at the end. A length of 3' is given on the scale, the 
divisions being marked in the groove. One foot of the scale 
is graduated into inches and these into halves, quarters, and 
eighths, each division on the scale representing \" - For dimen- 
sions smaller than J" ', approximations may be made as already 
described. 

(3) A scale of one-eighth size, or ij" = i', is the next smaller 
scale, and is given on the same flat with the 3" scale, the designating 
figure, 1 J, being at the opposite end. This scale is graduated to 
5' in length, the figures being stamped on the flat of the rule; 
i' is graduated into inches and these into halves and quarters. 
Smaller divisions may be approximated as above. 

With the foregoing explanation as a key, and remembering 
that when viewing a scale, if it is on the right-hand end of the rule 



102 



MECHANICAL DRAWING. 



the foot divisions are stamped in the groove, and if on the left- 
hand end, the figures are on the flat of the rule, the remaining 
eight scales may be interpreted. They are: 

(4) Scale of i" = i', =- f \ size, smallest divisions of which = J". 



(5) ' 


( I i 


3" _ T / 

4 ~~ L i 


1 
16 


u it 


tt 


i i 


i 1 


_ 1// 

2 


(6) ' 


t i I 


Iff _ T / 


-A 


it 11 


tt 


tt 


(i 


= l" 


(7) ' 


t It 


3"__ T f 
8 ~ L J 


— 1 « 
32 


t <t 


tt 


tt 


a 


= l" 


(8) ' 


t it 


Iff — T f 
4 —1 > 


— 1 * 
48 


( (( 


tt 


It 


tt 


= l" 


(9) ' 


1 it 


3 ft _ T f 

T6" ~ L J 


1 < 
— 6T 


;t it 


tt 


tt 


tt 


= l" 


(10) ' 


t tt 


1"_ T f 

8 ~ L i 


_ 1 < 

~12 


t tt 


tt 


tt 


tt 


= l" 


(11) ' 


t It 


3 ff — T f 

3 J ~ I > 


1 < 
— 1T"8" 


c tt 


cc 


a 


n 


= 2" 



The scales given are the usual scales; however, should an odd 
scale be required, one may be constructed as follows: Let it be 
required to divide 1" into sixths (A, Fig. 55). The nearest division 




Fig. 55. 



given on the scale is the \" division of the full-sized scale; to use 
this, erect a perpendicular at one extremity of the 1" line, and 
with an inch division of the scale on the other extreme, radiate 
the scale from this latter point until a division ij", or f" away 
from the inch division, coincides with the perpendicular, or, better, 
with the perpendicular drawn, take a radius of ij" on the bow- 



DRAWING TOOLS AND MATERIALS. 103 

pencil, and with the free end of the line as a center, describe an 
arc intersecting the perpendicular in a point; joining this point 
and the center gives a line ij" long. Now on this line lay off 
J" divisions, which gives six divisions; dropping perpendiculars 
through these six points of division to the 1" line will give six 
equal divisions on the line, sixths of an inch. "B" illustrates a 
3" length divided into seven equal lengths by a similar method. 

The mistake should not be made of attempting to use the 
scales |" = i / , J //== i r , etc., for laying out three quarter- and half- 
sized drawings respectively, as an inspection of the scale will 
show the graduations to then read J", J", ^V, 2V f° r the f" 
scale and J", J", T y for the \" scale, which divisions are 
odd and seldom used. Any scale may be doubled, tripled, 
quadrupled, etc.; for example, double the i" = i' scale; this 
changes the smallest division from J" to \" and gives a scale of 
2" = i' f or one-sixth size. 

The architect's scale is one of the "fine" tools, the gradu- 
ations being accurate, and in using it much care should be exer- 
cised to preserve the sharpness of its edges and the clearness of 
the graduations. 

To properly use the scale, lay it flat on the paper, with the 
scale in use from the body and in good light, and lay off the 
divisions with a fine-pointed pencil or metal point, being careful 
not to bring a pressure on the pencil sufficient to dent the surface 
of the paper, or using the metal point, do not puncture the paper 
to a depth which would mar the surface. Do not use metal 
points on the scale, or use it as a guide for ruling or cutting. 

101. Thumb-tacks. — "Thumb-tack" is the name given a 
large-headed small tack specially designed for temporarily fasten- 
ing paper or cloth to wood; they are used in drawing to fasten 
the drawing-paper or tracing- cloth to the drawing-board. The 
one essential of a satisfactory thumb-tack is that it have a head 
of sufficient area to prevent it tearing through the paper or cloth, 
and that it be so fashioned as not to be an obstacle to the free 
movement of the T-square and triangles over the surface of the 
drawing. 



104 MECHANICAL DRAWING. 

The ordinary tack-head is about g 1 /' to i y / thick and is more 
or less troublesome; to minimize the difficulty, 3-oz. or 4-oz. 
common tacks may be used, driven flush with the surface of the 
drawing-board ; the objection to this practice is that the small 
head of such a tack is not of sufficient area to retain the paper. 
As the student becomes more and more expert in the manipula- 
tion of his tools, the average thumb-tack ceases to be troublesome. 

102. Pencils and Leads.— A drawing is always first con- 
structed in pencil, then finished in ink. "What is the best draw- 
ing-pencil" is a question on which every draughtsman has his 
own private opinion. The degree of hardness of lead best adapted 
to the work is largely dependent upon the nature of the surface to be 
penciled on ; generalizing, paper is best worked with a hard 
lead and cloth with a soft lead. For paper a 6-H (trade name) 
pencil is recommended, while for cloth good results are obtained 
with a 2-H pencil. 

Penciling a drawing is like laying the foundation of a house: 
it is the basis upon which the building is done, and any inaccuracy 
in the penciling will appear in the finished drawing. In pen- 
ciling all lines are made practically of the same weight, which 
weight is a line just sufficiently heavy to stand out clear and 
distinct. 

To secure nice, clean-cut lines, the pencil-point should be 
given careful attention, never being allowed to become rough or 
dulled. There are several styles of points given leads, the three 
most prominent being (1) the round or needle point, (2) the fiat 
or chisel point, and' (3) the bevel or one-sided point. 

(1) The round or needle point is the most common and has 
the widest range of usefulness, being fairly well adapted for all 
ordinary drawing; it is, however, especially convenient for mark- 
ing points and for all free-hand work, such as free-hand lettering, 
dimensioning, etc. To fashion the needle-point, begin at a 
point about ij" from the end, and with a sharp knife bring it 
(the pencil end) to a neat and true cone, from the apex of which 
the lead projects about J"; now bring the lead to a uniformly 
tapered needle-point, and finish by spinning the pencil-point in a 



DRAWING TOOLS AND MATERIALS. 



I°5 



cloth held about it, thus removing all roughness and producing a 
fine, smooth point. This pointing of the lead is best accom- 






^> 



Fig. 56 

plished with the aid of a piece of fine sandpaper or emery-cloth 
(the latter is the better), by drawing the pencil-point over the 
surface of the paper or cloth and turning it at the same time 
until ground to a point. In any case the point should be "pol- 
shed off" with a rag, as described. 

To facilitate such use of sandpaper or emery-cloth, it should 
be stretched over a flat surface and securely fastened. A good 
arrangement is obtained by making a small paddle of wood and 
gluing the abrasive to its faces, or, better, as the paper and cloth 
soon become dull and unfit for further use (in the order named), 
it is well to make a pad of the material, then as one sheet becomes 
dulled it can be removed and a new, sharp sheet is presented. 

(2) The flat or chisel-pointed lead is restricted to the drawing 
of very fine lines, and is for accurate work, being especially 
adapted to the graphic solution of problems. To fashion the 
chisel-point, begin at a point about ij" from the end, and with a 
sharp knife bring two sides to a smooth and even bevel, with the 
lead extending about \" from the end of the bevel; next bring 
the remaining faces of the pencil to a smooth and true bevel to 
within about J" of the end of the lead, and then with knife or 
pad continue the first two bevels until the lead is very sharp and 
finish with a cloth, slightly rounding (lengthwise) the point 



Io6 MECHANICAL DRAWING. 

To have the needle and chisel- points always at hand, it is well 
to " double end" the drawing-pencil, one style point on each end. 
The two points described are primarily for the pencil-point only> 
though leads used in the compass and bow-pencil may be simi- 
larly fashioned, in which case the chisel-point should be adjusted 
in the instrument with a broad side next to the center-point. 

(3) The bevel or one sided point is especially designed for the 
lead points used in the instruments, and is fashioned by beginning 
at a point about \" from the end of the lead, and with knife or 
pad making a smooth, true bevel on one side only and entirely 
across the lead; the point is then finished with a cloth. The 
lead is adjusted in the tool with the center of the straight side 
next to the center-point. 

When ruling, the pencil should be held in a manner similar 
to that described for the ruling-pen, and especial attention given 
to maintaining one position throughout, that the lines may be 
exact, right lines. 

103. Pens and Penholders. — The selection of a pen is largely a 
matter of preference for some particular brand, though the " style" 
of pen is determined by the nature of the work to be done; for 
etching and for all small, fine work a lithographic crow-quill pen 
is the best, for all ordinary work, as lettering and sketching, any 
ordinary fine-pointed pen will answer, and for heavy work, as 
large lettering for titles, a ball- pointed or other heavy pen is recom- 
mended. From the first to the last are many points of various 
degrees of fineness, and that pen best suited to the work in hand 
is readily determined after a short experience. 

The one requisite for a good penholder is that it be of a size 
and shape to fit the hand without cramping; avoid all very small 
penholders. The pen should be firmly secured in the holder. 

The beginner should provide himself with at least three pen- 
points: (1) a crow-quill, (2) a common writing-pen, and (3) a 
ball -pointed pen; with these he will be equipped for this course 
and for all usual drawing. A new pen will always prove more or 
less troublesome, as the ink will not flow freely, and requires ta 
be " broken in." 



DRAWING TOOLS AND MATERIALS. 107 

The pen is one of the draughtsman's tools, and as such should 
receive proper care and attention; do not treat it roughly because 
it is "just a common pen" and is cheap. To have a good pen it 
must be first broken in, then preserved. The pen should always 
be carefully wiped with a rag free from lint or fuzz before laying 
it aside; never lay a pen down without wiping it off. 

104. Erasers. — In constructing a drawing a large number of 
pencil-lines are drawn which are not to appear on the finished 
drawing and must be erased; also, errors may be made in inking- 
in a drawing, necessitating an erasure; alterations on a finished 
drawing may be desired, which involves erasures, etc.; thus it is 
that a drawing outfit is incomplete without some means of erasing 
pencil and ink lines. 

An outfit should contain at least two erasers: (1) a pencil 
eraser, and (2) an ink eraser; a combination eraser, one end 
for pencil and one end for ink, will answer. The pencil eraser 
should be of soft rubber and possessed of a property which enables 
it to "take hold" on the paper; an eraser that is hard, gritty, or 
that has a glazed surface is unfit for erasing pencil-lines. 

An ink eraser should be hard and gritty, but should be pliable. 
All erasers after a time become hard and stiff and lose their 
erasive properties; an eraser should be much handled and 
"worked." 

For simply cleaning a sheet of paper, a third eraser known as 
a " sponge eraser " is very efficient and is a valuable addition to 
an outfit. 

105. Ink. — Until recent years it was customary for draughts- 
men to prepare their own ink from a stick of India or Chinese 
ink, by rubbing it in a specially designed saucer containing a 
small quantity of water. A very superior ink is thus produced, 
but the operation is quite laborious and time- consuming. 

The market of to-day affords a number of prepared inks, and 
from those a draughtsman's ink is usually selected. There are 
but two colors of ink much used in drawing: (1) black ink, and 
(2) red ink. 

Black drawing-ink differs from ordinary writing-fluid in that 



108 MECHANICAL DRAWING. 

it is heavier and less fluent. It is a form of carbon in suspension, 
and when applied to paper or cloth, leaves a deposit of carbon 
which is at once fixed and distinct. Drawing-ink is easily erased 
because of this deposit, as it is "on" the paper and not "in" it 
if the paper be a good drawing-paper. 

A good drawing ink has the carbon in perfect suspension, is 
smooth and even flowing, with no granular precipitation what- 
ever, and will produce clear and lasting lines. 

The red ink is more fluid than the black drawing-ink and 
requires great caution in its use, as it has a tendency to "run" 
from the pen onto the paper and under the edge of the T-square 
and triangles and cause blots. If a drawing is to be permanent, 
red "drawing ink" should be used (not a writing- fluid), as this, like 
the black ink, has the pigment in suspension and leaves a deposit 
on the paper. The objection to the use of red ink on drawings 
is that all red ink is more or less susceptible to the light and in 
time will fade; also, it is less opaque than the black ink and is 
not "printable," save to a degree, a fact which is sometimes 
taken advantage of in blue printing to render center lines and 
dimension lines lighter than lines of the drawing. 

106. Rag and Blotter. — A rag for cleaning instruments and 
wiping pens should be free from lint and fuzz and very absorp- 
tive. The cloth most acceptably fulfilling these requirements is an 
old linen or muslin rag. 

An ordinary blotter is an often needed article when drawing; 
not to blot the lines, however, as these must be allowed to dry, 
but to assist in removing blots. 

107. Horn Center. — The horn center is a device of some 
transparent material- designed to be fixed over a center- point 
and to receive the needle-point of the instrument when drawing 
a large number of concentric circles, thus avoiding a puncture 
of the paper. Such marring of the surface of a drawing is 
avoided without the use of a horn center with ordinary care, 
and they are only needed when a handsome, line- shaded drawing 
is attempted. 

108. Section -liners. — "Section -liner" is the name given a 



DRAWING TOOLS AND MATERIALS. 109 

machine for accurately cross-hatching surfaces. It is a convenient 
but costly device, and as cross-hatching is done in a number of 
abbreviated forms and is not required to be accurate a section- 
liner is not a necessity to the draughtsman. 

109. Erasing-shields. — This is a device of thin material, 
amber and various metals, with various shaped and sized open- 
ings, designed to mat out portions of a drawing to be erased. 

no. Protractors. — A protractor is a device graduated in 
degrees, and is used in laying off angles not obtainable with the 
triangles and T-square. Protractors may be had of various 
materials, the best being of metal. 

in. Scale-guard. — A scale-guard is an attachment for the 
triangular scale and is of use when one scale only is in constant 
use, as it enables the draughtsman to keep that scale always 
before him. 

112. Proportional Divider. — The proportional divider is a 
double-ended pair of dividers provided with an adjustable 
clamp which enables the draughtsman to set one end of the tool 
at full size, and by means of the adjustment the other end is 
made to be some proportional size, as \ size, \ size, etc. Their 
use is obvious. 

113. Erasing-knives. — Erasing-knives are a valuable addition 
to a drawing outfit; but as most draughtsmen are possessed of a 
pocket-knife, such a knife, well sharpened, answers all practical 
purposes. 

114. Soapstone Pencil. — Soapstone is used to resurface the 
surface of tracing- cloth after an erasure has been made. 

115. Paper. — Having discussed ways and means of con- 
structing drawings, it now becomes necessary to select some 
material on which to construct the drawings. For this purpose 
any smooth surface will answer, shopmen often using the shop 
floor, a board, the wall, a blackboard, etc., for rough, free-hand, 
temporary sketches; however, the draughtsman's work is sup- 
posed to have finish, accuracy, to be permanent, in short, to be 
valuable, and for his purposes the field is limited to cloth and to 
paper. 



no MECHANICAL DRAWING. 

All sketches, preliminary draughts, etc., are nearly always 
made on paper, cloth being reserved for the finished drawing, 
especially when the drawing is to be duplicated, as by blue print- 
ing. 

The selection of the quality of paper and its dimensions is 
determined by the nature of the work to be done. Broadly 
speaking, if the paper be intended for preliminary work, a cheap, 
low-grade paper will answer; while if the work is to be a finished 
and permanent article, an expensive, high-grade paper should 
be used. For the greatest permanency, a high-grade paper 
mounted on cloth is recommended. 

A good drawing-paper should be of a color to cause the lines 
to stand out sharply (in contrast) and the color should be perma- 
nent, the light having no effect upon it. It should have a hard, 
smooth, and even surface, taking pencil and ink lines sharply, the 
latter' without any tendency to spread or blot, and should take 
erasures to quite an extent. Added to this, it is quite desirable, 
for all usual purposes, that the paper should have some body — ■ 
be rather stiff — thus minimizing any tendency to wrinkle or to 
buckle. 

The paper most nearly fulfilling the above requirements 
is a pure rag or linen, hot-pressed paper, white in color. It 
should be understood this applies only to paper for good, per- 
manent, inked drawings; for pencil work and work that is to be 
traced, any paper that has body and will take erasures will answer. 

As has already been noted, the size of the paper is determined 
by the size of the work to be done. Paper is furnished by the 
trade in two forms, (i) sheets and (2) in rolls, the dimensions 
for sheets being: 

Medium i7 ,, X22 ,/ 

Royal io"X24" 

Imperial 22" X 30' 

Double elephant 27"X40 / 



>" 



While rolls of almost any length and from 2 ft. to 6 ft. wide 
may be had, only the finer grades of paper are offered in sheet 



DRAWING TOOLS AND MATERIALS. in 

form, though any roll paper will be cut to order. Sheet paper is 
sold at so much per sheet, ream, and quire; roll paper at so much 
per yard of certain width, and some grades by the hundred 
pounds. 

In draughting-rooms, where all work is traced, it is customary 
to use roll paper of suitable width, the draughtsman tearing off 
such amounts as needed. 

If sheet paper is to be used, that size should be selected which 
reduces waste to a minimum. For example, let it be required to 
furnish paper to cut into o/'xi2" sheets; the Royal, iq"X24", 
sheet will be found to four- fold into 9j"Xi2", giving four sheets 
of these dimensions, each sheet having J"Xi2" waste, an amount 
which when divided in two will give \" waste at the top and 
bottom of the sheet, sufficient to cut out the thumb-tack holes; 
this is the size of paper required for the drawings of this course. 

116. To Make Erasures on Paper. — The quality of the paper 
being right, the labor of neatly removing pencil lines is directly 
dependent upon the character of the penciling. For the best 
results, the penciling should be done with a fine-pointed, hard 
lead, and the lines made very light, just sufficiently heavy to be 
clean-cut and clear. To do this the pencil must be handled very 
lightly and no crease made in the surface of the paper, a case 
wherein the pencil-mark may be removed, but not the crease. 
To make the erasure, lightly rub the pencil eraser over the line 
until it disappears, and then with a cloth dust off the paper. 
When working on high-grade paper, this last item is of great im- 
portance, for if the paper be not dusted and the erasure be per- 
mitted to remain on the surface, it will soon become ground 
into the paper and cannot then be clearly removed. 

To make ink erasures on paper, it is best to use the ink eraser 
and with considerable pressure rub the line to be removed until 
it is quite indistinct, then dust off the surface, and finish, as above 
described, with the pencil eraser and again dust off; such a 
treatment well applied should leave a surface uniform with the 
remainder of the sheet, and one that will again take ink without 
any resurfacing of the spot. If the line to be removed be a heavy 



H2 MECHANICAL DRAWING. 

one, it will facilitate the operation if the erasing-knife be first 
applied. To do this, hold the knife-blade in a plane perpen- 
dicular to the line and lightly scratch the ink deposit until it 
becomes quite dim, then proceed with ink and pencil erasers. 
Great care must be exercised when using the knife not to dig 
into the paper or to scuff the surface. 

117. Profile and Cross-section Paper. — These are specially 
ruled papers, much used for plotting and for sketch-work. 

118. Tracing-paper. — Tracing-paper is comparatively thin 
paper, specially treated to render it transparent, and is used as 
a substitute for tracing-cloth, because of its lesser cost. Trans- 
parent profile and cross-section paper may be had of the trade. 

In most paper there is a right and a wrong side to it; that side 
which presents the smoothest surface should be used. 

119. Blue-print Paper. — This is a specially prepared paper 
used for reproducing drawings, for making blue-prints, a white 
line on a blue background. The paper is coated with a solution 
of certain salts which are susceptible to the sun's rays, an expos- 
ure thereto causing the prepared surface to undergo a change. 

Prepared paper may also be had which will give blue lines on 
a white background, and several other contrasts. 

Blue-print paper is, comparatively, a cheap commodity, and is 
supplied by the trade in various qualities, sizes — usually in 10-yd. 
rolls of variable widths — and degrees of sensitiveness, from the 
extra-rapid printing to the five- and ten-minute paper. 

The paper can be bought, ordinarily, cheaper than it can be 
made, and when thus obtained is of uniform quality; however, 
should it be desired to prepare some paper, the following formula 
is recommended: Dissolve 5 oz. (avoirdupois) of red prussiate 
of potash in 32 oz. (fluid) of rain-water, permit it to stand for 
two or three days, then filter. When ready to use, for every 
200 sq. ft. of paper dissolve 1 oz. (avoirdupois) of citrate of 
iron and ammonia in 4J oz. (fluid) of rain-water and mix the 
two solutions in equal volumes. Any paper with a smooth, 
hard surface may be used and the solution applied with a sponge, 
care being taken to give the surface a smooth and even coating, 



DRAWING TOOLS AND MATERIALS. "3 

or the paper may be floated on a basin filled with the solution 
and thus coated. If both sides are to be prepared for printing, 
the paper can be dipped in the solution. After the surface has 
been coated, the paper should be hung up in a dark place to 
dry, and when dry is ready for use. It is obvious the paper 
must be protected from the sunlight until ready to use. 

The above solution, for the best results, should be given three 
or four minutes in a bright sunlight. 

Linen fabric is also prepared for printing purposes. ' 

120. Tracing-cloth.— Tracing-cloth, or tracing-linen, is smooth, 
thin, linen cloth which has been treated with "size," one side 
being finished with a glazed surface and the other in the rough. 
It is very transparent and is used for tracing drawings, the com- 
mon practice of the day being to trace all permanent work, the 
cloth being less destructible than paper, and being transparent, 
the drawing can be reproduced by blue-printing. 

"Which side of the cloth is the best for use" is a much dis- 
cussed question, each side having its advantages. The smooth 
side takes erasures the better, that is, erasures may be made on 
this side more easily than on the rough side; the smooth side is 
a trifle the better for free-hand work, such as lettering, dimen- 
sioning, etc., but when drawings are made on this surface, the 
cloth has a tendency to curl up, a very troublesome feature. The 
major arguments for the preference of the rough side are: It 
takes the ink better, can be penciled on also, and the tendency to 
curl up is a minimum. With a little practice and care, erasures 
can be readily and neatly made on this side of the cloth, and 
for general purposes, the writer advocates the use of the rough 
surface. 

To use the cloth, stretch it taut, smooth, and even over the 
drawing to be traced and proceed as when inking on paper. 
Should the ink have a tendency to skip or be ragged, the cause 
may be removed by rubbing chalk dust over the surface and 
then polishing it off. 

121. To Make an Erasure on Tracing-cloth. — To erase ink 
from tracing-cloth, use the erasing-knife as described for eras- 



H4 MECHANICAL DRAWING. 

ing on paper until the line is quite dim; then the ink eraser, 
followed by the pencil eraser; then resurface the spot erased by 
rubbing the surface with soapstone and polish with a cloth. 
The tracing-cloth can then be again inked on without any ten- 
dency to blot. 

To remove pencil-lines and to clean tracing- cloth apply a 
rag saturated with gasoline or benzine. 

No water should be allowed to get on the cloth, as it destroys 
the surface and renders it unfit for use. 

Tracing-cloth is supplied by the trade in the form of rolls of 
various lengths and widths. 



CHAPTER V. 

THE REPRODUCTION OF DRAWINGS. 

I22 Introductory. — Mechanical drawing is an art to facilitate 
manufacture. No longer is the construction of a bit of mechanism, 
a machine, a dwelling-house, a bridge, etc., a "cut and try" 
operation; rather, have such undertakings become "exact sciences " 
because of drawing and design. When such works are now pro- 
posed, the entire scheme is worked out beforehand to the smallest 
detail; drawings of all the parts or works are made, forming 
what is called the "plans" for the undertaking, which, together 
with any necessary additional information, called the "specifica- 
tions," forms a safe, accurate, and complete guide for the work. 

Let it be assumed that a machine , is to be produced; the 
design having been worked out, accurate mechanical draw- 
ings of the machine as a whole, and of its component parts, are 
drawn to scale; these drawings are to be the "guide" for the 
artisan in his work; that is, the shopman must have "something 
to go by." Should the original drawings be sent into the shop it 
is quite probable that they would soon become soiled and illegible 
in the grimy hands of the workman and the design lost. The 
production of the drawings has cost the manufacturer a con- 
siderable sum of money and he can ill afford to have original 
drawings go into the shop; the universal practice is to furnish 
a duplicate drawing to the workmen and to keep the original on 
file in the draughting-room. 

Besides the reason cited above, the manufacturer must pre- 
serve the drawings as a "receipt" for the undertaking in case 
of future orders for the same design; also, the drawings may 
be needed at different points at the same time; for these and 

ri5 



n6 MECHANICAL DRAWING. 

many other obvious reasons it is necessary that original drawings 
be duplicated and the originals preserved. 

An exception to the foregoing is the occasional practice of 
mounting original drawings on cardboard, sheet iron, wood, etc., 
protecting the drawings with a glass cover, a coat of varnish, 
shellac, etc., then sending them into the shop. Such a practice 
is limited, and is usually employed where the work is stand- 
ard — tables of standards, shop-cards, etc. — and the drawings are 
needed permanently in one place. 

Drawings may be duplicated in various ways, principal 
among which are by blue-print process, by photography, by the 
hectograph and similar processes, and by the mimeograph, being 
named in the order of their importance for practical pai poses. 

123. Blue-printing. — Blue-printing is the almost universal 
method of reproducing drawings for practical purposes, the draw- 
ings being made on tracing linen. By this method an unlimited 
number of duplicates may be made, the most serious objection 
to the practice being that good sunlight is required for the print- 
ing, an erstwhile, very serious objection when it is remembered 
that during the winter months the sun does not shine for days 
at a time; however, this objection is eliminated by the present- 
day practice of printing by electric light, and minimized to quite 
a degree by rapid printing paper which will print in a compara- 
tively short time on the darkest of days. The operation is a 
very cheap one, and a good blue- print is both beautiful and clear 
to the eye; it does not show dirt and is admirably adapted for 
use in the shop. 

To duplicate a drawing by this process requires the use of 
some such printing-frame as is depicted on page 188, the pro- 
cedure being as follows: With the back of the printing- frame 
removed, place the drawing (tracing) in the frame with the inked 
side next to the glass; next place the prepared paper in the frame 
with the prepared side next to the tracing, close the frame by 
putting the back in position, and see that it is well secured by 
the springs and catches; this done, carefully inspect the drawing - 
and print-paper (through the glass front) and see that they have 



REPRODUCTION OF DRAWINGS. 117 

good contact with each other and with the glass and are free from 
folds and wrinkles; when the arrangement passes inspection expose 
the frame to the sun in a position as nearly at right angles to its 
rays as is possible and for a length of time suitable to the paper, 
then remove the paper (not the tracing) and wash it (the paper) 
for three or four minutes in a bath of clear water and then hang it 
up to dry. 

The explanation of the phenomenon is, the paper is sensi- 
tized with a preparation which is susceptible to the sunlight, and 
when the printing-frame is exposed, all parts of the print-paper 
exposed to the sun are affected by its rays. Not so with those 
portions of the paper directly beneath the lines of the drawing; 
these are protected from the sun by the opaque deposit of ink on 
the tracing- cloth and this leaves a design on the paper — the 
duplicate of the tracing— unaffected by the sunlight. Should the 
printing proceed beyond the proper time exposure, the sun's rays 
will gradually pierce the lines of the drawing and the entire sur- 
face of the paper will become affected, presenting a uniform field 
and no " print"; also, should the exposure not be of the proper 
length of time, the paper will not be acted on by the sunlight 
long enough to produce sufficient contrast and again give a uniform 
field and no " print." 

From the above it is evident that there is a limited exposure 
necessary for good results; also that it is then necessary to in 
some manner "fix" the print, rendering it immune to further 
exposures; this is done by the water-bath, the water "fixing" 
the exposed surface and dissolving the preparation from the 
unexposed design. The paper used for the production of the 
process paper is originally a white paper; when sensitized, a 
dull-gray or greenish color; when exposed, a deep gray, and 
when washed, a shade of blue, from light to dark according to the 
length of the exposure. The protected parts remain the original 
dull-gray or greenish color, and when washed present the white 
paper beneath, thus giving white lines on a blue background, 
the ordinary blue-print. 

124. Exposure. — If an exposure results in an entire very 



ti8 MECHANICAL DRAWING. 

deep-blue field, the exposure has been too long, or else the lines 
*>f the drawing were transparent, the ink used unfit for printing 
purposes; if the result be a light, milky- looking print, the exposure 
was of too short duration. " The newer the paper the longer to 
print and quicker to wash; the older the paper the quicker to 
print and longer to wash." 

125. Washing. — The washing of the prints is a very par- 
ticular step in the process, as a too long washing will have a 
tendency to wash out the print, ultimately dissolving all of the 
preparation and presenting the original white paper; a short 
bath does not give sufficient time for the water to completely 
dissolve the preparation from the unexposed parts of the paper, 
arid when again exposed to light (in use) the print will soon 
succumb to the sun's rays and the design fade away. 

Prints may be kept in a dark place for quite a length of time 
before being washed, though it is preferable to wash them soon 
after printing. 

126. Drying.— For drying prints, the best results are obtained 
hy "hanging up"; a good arrangement is a frame containing a 
number of "clip" fasteners — spring clothes pins. When dry the 
print will be more or less 'curled up"; to straighten, draw it 
t>ver a sharp table- edge two or three times, or take it down 
while yet a little moist and place i: in a press. 

A print when once made is a permanent "job" and any 
corrections or alterations should be made on the tracing and a 
Iiew print made. However, if the desired change be not of much 
import and not requiring much labor, the print may be marked on 
with a solution of common washing soda and water. 

After some experience one is able to judge of the proper expos- 
ure for a paper by the change in color of the preparation. When 
\ising such a frame as shown on page 188, the paper may be in 
spected by raising one part of the two-part back and noting the 
•change in color; if under-exposed, the frame can be closed again 
and the exposure continued, the tracing and paper having been 
held in position by the closed half of the back. If no such frame 
Is to be had, a test piece of paper may be placed in one corner of 



REPRODUCTION OF DRAWINGS. 119 

the frame and exposed along with the tracing, and when this 
is of the proper color the paper should be removed and washed. 

127. Photography. — The art of reproducing by photography 
is a branch of the "trade" of photography. Under this heading 
is also included the various photogravure processes by which 
plates are produced for press-printing. This is the method 
employed by the publishers of text-books, technical papers, 
magazines, etc., and while of vast importance in this field, it has 
a small place in the field of manufacture. 

128. The Hectograph. — The hectograph process of duplicat- 
ing drawings is a process much used by architects and others 
when but a limited number of copies are required. It has the 
advantage of producing drawings in colors. The drawing is 
made on smooth paper with specially prepared aniline inks, 
and is then copied on the hectograph — a slab coated with gela- 
tin — by pressing the drawing on its surface, thus transferring 
part of the ink from the drawing to the gelatin of the pad, where 
it is retained after the original has been removed. To make a 
copy, blank paper is pressed on the surface of the hectograph 
and well rubbed so that the contact is perfect, when the gelatin, 
giving up part of the ink deposit, gives an exact copy in colors 
of the original drawing. The copy is then removed from the pad 
and when dry is ready for use. 

129. The Mimeograph. — The mimeograph has no commer^ 
cial rating as a copying process for mechanical drawings for 
shop purposes, but is valuable as a means for duplicating notes, 
small and fairly simple diagrams, etc. A very large number 
of copies are to be had by this process. The drawing or copy,- 
is made on a specially prepared paper by moving a pointed stylus,, 
as in drawing or writing, over the paper when on a finely grooved, 
steel plate, thus tracing the copy in a series of minute perforations.. 
The stencil is then suspended in a special frame, and by means; 
of an ink-roller, ink is forced through the perforations onto blank- 
paper placed beneath the stencil, producing a fac-simile of the 
stencil. Stencils may also be made on a typewriter. 



CHAPTER VI. 

PATENT-OFFICE DRAWINGS* 

130. Introductory. — Draughtsmen are often called upon to 
execute drawings for presentation to the United States Patent 
Office, and that the requisites of that office and method of pro- 
cedure may be known, the following remarks are taken from the 
"Rules of Practice in the United States Patent Office." 

131. Drawings. — The applicant for a patent is required by 
law to furnish a drawing of his invention whenever the nature of 
the case admits of it. 

132. Requisites of Drawings. — The drawing may be signed 
by the inventor, or the name of the inventor may be signed on 
the drawing by his attorney in fact, and must be attested by two 
witnesses. The drawing must show every feature of the inven- 
tion covered by the claims, and the figures should be consecu- 
tively numbered if possible. When the invention consists of 
an improvement on an old machine the drawing must exhibit, 
in one or more views, the invention itself disconnected from the 
old structure, and also in another view so much only of the old 
structure as will suffice to show the connection of the invention 
therewith. 

133. Three Editions of Drawings. — Three several editions of 
patent drawings are printed and published: one for office use, 
certified copies, etc., of the size and character of those attached 
to patents, the work being about six by nine and one-half inches; 
one reduced to half that scale, or one-fourth the surface, of which 
four are printed on a page to illustrate the volumes distributed 
to the courts; and one reduction — to about the same scale— 
of a selected portion of each drawing for the Official Gazette. 

— - ■ — - -- ■ ■ - 

* Extract from "Rules of Practice in the United States Patent Office." 

120 



PATENT OFFICE DRAWINGS. 121 

134. Uniform Standard.— This work is done by the photo- 
lithographic process, and therefore the character of each original 
drawing must be brought as nearly as possible to a uniform 
standard of excellence, suited to the requirements of the process 
and calculated to give the best results in the interests of inventors, 
of the office, and of the public The following rules will there- 
fore be rigidly enforced, and any departure from them will be 
certain to cause delay in the examination of an application for 
letters patent: 

135. Paper and Ink. — (1) Drawings must be made upon pure 
white paper of a thickness corresponding to three- sheet Bristol - 
board. The surface of the paper must be calendered and smooth. 
India ink alone must be used, to secure perfectly black and 
solid lines. 

136. Size of Sheet and Marginal Lines. — (2) The size of a 
sheet on which a drawing is made must be exactly ten by fifteen 
inches. One. inch from its edges a single marginal line is to be 
drawn, leaving the "sight" precisely eight by thirteen inches. 
Within this m:rgin all work and signatures must be included. 
One of the shorter sides of the sheet is regarded as its top, and 
measuring downwardly from the marginal line a space of not 
less than one and one-quarter inches is to be left blank for the 
heading of title, name, number, and date. 

137. Character and Color of Lines. — (3) All drawings must 
be made with the pen only. Every line and letter (signatures 
included) must be absolutely black. This direction applies to all 
lines, however fine, to shading, and to lines representing cut 
surfaces in sectional views. All lines must be clean, sharp, and 
solid, and they must not be too fine or crowded. Surface shad- 
ing, when used, should be open. Sectional shading should be 
made by oblique parallel lines, which may be about one- twentieth 
of an inch apart. Solid black should not be used for sectional 
or surface shading. 

138. Few Lines and Little or No Shading. — (4) Drawings 
should be made with the fewest possible lines consistent with 
clearness. By the observance of this rule the effectiveness of 



122 MECHANICAL DRAlVING. 

the work after reduction will be much increased. Shading 
(except on sectional views) should be used only on convex and 
concave surfaces, where it should be used sparingly, and may 
even there be dispensed with if the drawing is otherwise well 
executed. The plane upon which a sectional view is taken 
should be indicated on the general view by a broken or dotted 
line. Heavy lines on the shade sides of objects should be used, 
except where they tend to thicken the work and obscure letters 
of reference. The light is always supposed, to come from the 
upper left-hand corner at an angle of forty-five degrees. Imita- 
tions of wood or surface graining should not be attempted. 

139. Scale of the Drawing. — (5) The scale to which a draw- 
ing is made ought to be large enough to show the mechanism 
without crowding, and two or more sheets should be used if one 
does not give sufficient room to accomplish this end; but the 
number of sheets must never be more than is absolutely neces- 
sary. 

140. Letters of Reference. — (6) The different views should 
be consecutively numbered. Letters and figures of reference 
must be carefully formed. They should, if possible, measure at 
least one-eighth of an inch in height, so that they may bear re- 
duction to one twenty-fourth of an inch; they may be much larger 
when there is sufficient room. They must be so placed in the close 
and complex parts of drawings as not to interfere with a thorough 
comprehension of the same, and therefore should rarely cross 
or mingle with the lines. When necessarily grouped around a 
certain part, they should be placed at a little distance, where 
there is available space, and connected by short broken lines 
with the parts to which they refer. They must never appear 
upon shaded surfaces, and when it is difficult to avoid this, a 
blank space must be left in the shading where the letter occurs, 
so that it shall appear perfectly distinct and separate from the 
work. If the same part of an invention appear in more than 
one view of the drawing it must always be represented by the 
same character, and the same character must never be used to 
designate different parts. 



PATENT-OFFICE DRAWINGS. 



123 



PLATE No. ia 



U.S. PATEN T OFFICE CON VENTIONS 



Wood or Metal 



Liquid 







Glass 




'ffi 


'mm 


y2$//yy%Yyr 


HI 



Sandstone 



wmm, 



wm f mv/mmm 



Earth 




Sect, ot Insulation 



Coarse & Fine FaDric 



Cement 

Cork 
Insulation 





Yellow Red 



Blue Green Purple Black Orange 





Tri-Phase Connections 



— WVWVW— I 

Resistance 
Fuse Inductive Resistance 





Variable Resistance 




Off 



On 



6666066 



Incandescent Incandescent Circuit 



Pole Changer Switch 



xm=> 



Adjustable Ind. Resistance 



Transmitter 



Ground 



Solonoid Condenser v 



_^^ 



Crossing Wires 
Joined'Wires 

x x x x x H db 

Arc Lamps plus Minus Plus or Minus 



124 MECHANICAL DRAWING* 

141. Signatures of Inventor and Witnesses. — (7) The signa- 
ture of the inventor should be placed at the lower right-hand 
corner of each sheet, and the signatures of the witnesses at the 
lower left-hand corner, all within the marginal line, but in no 
instance should they trespass upon the drawings. 

142. Title. — The title should be written with pencil on the 
back of the sheet. The permanent names and title will be 
supplied subsequently by the office in uniform style. 

143. Large Views. — When views are longer than the width 
of the sheet, the sheet should be turned on its side, and the head- 
ing will be placed at the right and the signatures at the left, occupy- 
ing the same space and position as in the upright views, and being 
horizontal when the sheet is held in an upright position; and 
all views on the same sheet must stand in the same direction. 
One figure must not be placed upon another or within the outline 
of another. 

144. Figure for Gazette. — 8) As a rule, one view only of 
each invention can be shown in the Gazette illustrations. The 
selection of that portion of a drawing best calculated to explain 
the nature of the specific improvement would be facilitated and 
the final result improved by the Judicious execution of a figure 
with express reference to the Gazette, but which might at the 
same time serve as one of the figures referred to in the specifica- 
tion. For this purpose the figure may be a plan, elevation, sec- 
tion, or perspective view, according to the judgment of the 
draughtsman. It must not cover a space exceeding 16 sq. ins. 
All its parts should be especially open and distinct, with very 
little or no shading, and it must illustrate the invention claimed 
only, to the exclusion of all other details. When well executed, 
it will be used without curtailment or change, but any excessive 
fineness, or crowding, or unnecessary elaborateness of detail will 
necessitate its exclusion from the Gazette. 

145. Drawings to be Rolled for Transmission. — (9) Drawings 
should be rolled for transmission to the office, not folded. 

146. No Stamp, Advertisement, or Address Permitted on the 
Face of Drawings. — An agent's or attorney's stamp or advertise- 



PATENT-OFFICE DRAWINGS. 125 

ment or written address will not be permitted upon the face of a 
drawing, within or without the marginal line. 

147. Drawings for Designs. — In certain cases these rules may 
be modified as to drawings for designs. 

148. Drawings for Reissue Applications. — All reissue appli- 
cations must be accompanied by new drawings of the character 
required in original applications, and the inventor's name must 
appear upon the same in all cases; and such drawings shall be 
made upon the same scale as the original drawing, or upon a 
larger scale, unless a reduction of scale shall be authorized by 
the Commissioner. 

149. Defective Drawings. — The foregoing rules relating to 
drawings will be rigidly enforced. Every drawing not artis- 
tically executed in conformity thereto may be admitted for pur- 
poses of examination if it sufficiently illustrates the invention, 
but in such cases a new drawing must be furnished before the 
application can be allowed. The office will make the necessary , 
corrections at the applicant's option and cost. 

150. Drawings Furnished by Office.— Applicants are advised 
to employ competent artists to make their drawings. 

The office will furnish the drawings at cost, as promptly as 
its draughtsman can make them, for applicants who cannot 
otherwise conveniently procure them. 



CHAPTER VII. 

GEARING. 

151. Introductory. — A gear-wheel is a wheel with teeth spaced 
around its circumference, and is used to transmit motion by 
rolling contact with other toothed wheels. Gear-wheels are 
much used in the construction of machinery, the planning for 
which means that they, like other details, must be worked out 
and pictured by the draughtsman- designer. 

The subject " Gear-wheels and Gearing" is one of much 
magnitude, there being several systems of forms of gear-teeth > 
many kinds of gear-wheels, and an endless arrangement of the 
various wheels. It forms a part of the study of "Mechanism"; 
however, as the draughtsman often has occasion to draw gear- 
wheels without any reference whatever to the " design, " the 
study of the usual forms of teeth is properly a part of this work. 
It is the purpose of these remarks to treat the subject from the 
draughtsman's standpoint, and, eliminating as much of the 
theory as is possible, to acquaint the student with the several 
forms of teeth and kinds of gears, and to instruct him how to 
draw them. 

152. Fundamental Curves. — As a preliminary, the student 
must acquaint himself with the elementary curves used to form 
the tooth curve and the manner of their construction. These 
curves, for the usual forms of teeth, are four in number, and are 
(1) the cycloid, (2) the epicycloid, (3) the hypocycloid, and (4) 
the involute. 

The Cycloid. — Fig. 57. If a circle be rolled along a straight 

line, every point in its circumference will describe a curve known 

as the cycloid. For example, assume a buggy-wheel rolling 

126 



GEARING. 



127 



along a level road, the travel of any particular point on the rim 
is a cycloid. 

To construct the curve, draw the indefinite straight line A -B 
as a base line, then draw the circle at the left of the diagram and 
divide its circumference into a number of equal arcs — twelve 




Fig. 57. 



being a good working number, though the greater the number 
the more nearly accurate the work becomes — as O-D, D-E, etc. 
Next lay off the lengths O-N', N'-M', etc., equal to the length 
of the arc O-D and erect the perpendiculars O-C, N f -C lf etc. 
[It will be noted that the circle is divided into an equal number 
of equal arcs; this facilitates the construction, as the lengths dealt 
with are uniform, and the curve may be laid out symmetrically 
with a center line (Z'-0 6 ). However, the circle may be divided 
in any manner, provided the various lengths be used properly.] 
Lastly, draw the lines /-/, J-H, etc., parallel to the base line 
A-B. Now assume the circle to roll to the right; when the 
point N has reached N', the center of the circle, C, has traveled 
to C x ; with this point as a center and the proper radius — that of 
the rolling circle — by describing an arc intersecting the line N-D, 
the point O is found to be at O x — the point O is the point taken 
for the example. By proceeding in this manner until the circle 
has traversed its circumference, and using the successive posi- 
tions of the center-point, C, a series of points, O, O v 2 , 3 , etc., 
are obtained through which the cycloid is drawn. 

The Epicycloid. — Fig. 58. If a circle be rolled around the 
outside of a fixed circle, every point in the circumference of the 
rolling circle will describe a curve known as the epicycloid. 

To construct the curve, draw the fixed circle A-B, then draw 



128 



MECHANICAL DRAWING. 



the rolling circle O-D-E, etc. (the circle at the extreme left of 
the diagram), and divide its circumference into an equal number 
of equal arcs, as O-D, D-E, etc. ; next lay off the arcs 0-N' } N'-M f 
etc., on the circumference of fixed circle A-B, equal to the arc 
O-D of the rolling circle, and draw the radial lines through 
these points; lastly, draw the circular arcs through the points 
of division on the circumference of the rolling circle and 
through its center. Now assume the circle to roll to the 
right; when the point N has reached N' f the center of the 
circle is at C L) and with this point as a center and with the 




Fig.58. 



proper radius — that of the rolling circle — by describing an arc 
intersecting the circular arc N-D, the point O is found to be at 
O v By thus rolling the circle to the right for a complete revo- 
lution, locating the successive positions of the center-point, 
C 1? C 2 , C 3 , etc., and describing the proper arcs, a series of 
points, O, Oj, 2 , etc., are obtained through which the epi- 
cycloid is drawn. 

The Hypocycloid. — If a circle be rolled around the inside 
of a fixed circle, every point in the circumference of the rolling 
circle will describe a curve known as the hypocycloid. 



GEARING. 



129 



The manner of constructing the curve is identical with that 
given for the epicycloid, as is clearly evident from Fig. 58. 

The Involute. — Fig. 59. If a straight line, or to be consistent, 
a circle of infinite radius be rolled around the outside of a fixed 
circle, every point in it will describe a curve known as the involute. 
A common illustration is to wind a string about a cylinder, then 
keeping the string taut, unwind it; the end of the string will 
describe an involute. 




Fig. 59. 



To construct the curve, draw the circle 1-2-3, e ^ c -) an d divide 
its circumference as shown; at each of these points of division 
draw a tangent to the circle, then lay off the lengths 2-1' equal 
to the arc 2-1, 3-1' equal to .the arc 3-1, etc.; that is, beginning 
at a certain point, the length of the tangent at any point must 
be equal to the length of the rectified arc between that point 
and the starting-point. 

153. Glossary of Terms. — The projections around the periph- 
ery of a gear-wheel are called the teeth of the gear; the blank 
spaces between the teeth are called the spaces. The width of a 
tooth plus the width of a space, measured on a certain circle 
called the pitch-circle, is called the circular pitch of the gear. 



130 MECHANICAL DRAWING. 

The engaging surface of a tooth projecting beyond the pitch- 
circle is called the face of the tooth; the engaging surface within the 
pitch-circle is called the flank of the tooth. That face of a tooth 
first coming into contact is called the front of the tooth; that 
face coming into contact later is called the back of the tooth; 
thus there is the front and back face of a tooth, and the front 
and back flank of a tooth. The point where the pitch-circle 
cuts the front of a tooth is called the pitch-point of the tooth. 
The outer end of a tooth is called the addendum end, and a 
circle, concentric with the gear, drawn through it is called the 
addendum- circle; the inner "end" of a tooth is called the root 
of the tooth, and a circle, concentric with the gear, drawn through 
it is called the root-circle. The space between the addendum- 
circle of one gear and the root-circle of the gear with which it 
engages is called the clearance of the gears; a circle defining the 
clearance of a gear is called the dedendum-circle. The depth of 
a tooth is the distance, measured radially, between the addendum- 
and root-circles of the gear. The fillet is the rounded part of 
the flank, fashioned so as to give the tooth strength. The pitch- 
diameter, or simply diameter of a gear, is the diameter of its pitch- 
circle; the diametral pitch of a gear is the ratio of the number of 
teeth to the pitch-diameter. The gear to which the power is 
applied is called the driver; the one with which it engages is 
called the follower. 

Gears are designated in two general ways: (1) by giving the 
pitch-diameter of the gear and number of teeth, as a 10" gear 
having 40 teeth; (2) by the pitch-diameter and diametral pitch 
of the gear, as (for the same gear) a 10" four-pitch gear. 

154. Usual Proportions for Teeth. — The dimensions of the 
teeth of a gear are determined in two ways: (1) by making them 
proportional to the circular pitch, and (2) by proportioning them 
to the diametral pitch. Both methods are much used; also, there 
are several proportions in use. For the draughtsman a good 
method is to draw the addendum .3 of the circular pitch, meas- 
ured radially out from the pitch-circle; the dedendum .3 of the 
circular pitch, measured in a like manner in from the pitch-circle ; 



GEARING. 131 

the clearance to be .1 of the circular pitch; the width of tooth 
and space to be equal and equal to one-half of the circular pitch. 

155. Development of Formulae. 
Let D = the diameter of the gear. 

C = the circumference of the gear =3.1416X^=^7?. 

iV = the number of teeth. 

C 
P = the circular pitch = -rj (1) 

N 
P' = the diametral pitch = — (2) 

Then, with the diameter and circular pitch given, to find the 
number of teeth, 

N =T (3) 

With the diameter and diametral pitch given, to find the 
number of teeth, 

N = P f D (4) 

Placing the two values of N equal to each other, 

C 

~p=P f D. 

Substituting xD for C, 

Hence 

P'=J (5) 

P=J, (6) 

7T=PP' (7) 

156. Kinds of Gears. — Of the several kinds of gears met 
with in practice, three have been chosen and will be discussed 
as being representative of those most frequently confronting 



132 MECHANICAL DRAWING. 

the draughtsman. 1. A spur -gear is a gear whose teeth are on 
the outside of the gear. 2. A rack is a spur-gear whose radius 
is infinity; here the pitch-circle becomes a pitch-line, the adden- 
dum-circle the addendum- line, etc. 3. An annular or internal 
gear is a gear whose teeth are on the inside of the gear.* 

157. Systems of Teeth. — Like the kinds of gears, there are 
several systems of tooth outline; of these but two are widely in 
use: (1) the cycloidal system, and (2) the involute system. 

The form of the tooth curve adopted for the rack is the deter- 
mining basis for the systems. If the tooth curve is composed 
of cycloidal curves, the resulting system is called the cycloidal 
system; when the tooth curve becomes a straight line the resulting 
system is called the involute system. 

In the cycloidal system the tooth curve is described by certain 
circles, called describing-circles, rolling on the pitch- circle of 
the gear; in the involute system the tooth curve is formed by the 
involute to a certain circle, called the base-circle, drawn tangent to 
a certain straight line, called the line 0] action, drawn through 
the common pitch-point of the two gears, and a radial line drawn 
from the origin of the involute. 

158. Interchangeability. — Gears are largely made to work 
in sets; for this reason it is necessary that the teeth be so fash- 
ioned that the gear will be interchangeable within certain limits. 

In the cycloidal system, if the gear is not to be one of a set, a 
good general rule is to make the diameter of the rolling circle 
equal to three-eighths of the diameter of the pitch- circle in which 
it rolls; if the gear is to be one of a set, a universal rule is to make 
the rolling circles for the set of a uniform diameter, this diameter 
to be equal to the radius of a gear with twelve teeth of the circular 
pitch of the set, the fundamental for all interchangeability being 
a uniform circular pitch. 

In the involute system the gears must have a common line of 
action and a uniform circular pitch. 

159. Methods of Drawing the Tooth Outline. — There are 
several practical methods for drawing the tooth curve; to treat of 
all of them is beyond the scope of this work, and the discussion 



GEARING. 



*ZZ 



will be limited to the two methods most widely in use. i. The 
"exact method" is the term applied to the procedure when the 
true theoretical tooth curve is drawn. 2. The " approximate 
method" is the term applied when the true tooth curve is approxi- 
mated. 

160. Spur-gears. Exact, Non-interchangeable Cycloidal. — 
Let it be assumed that the draughtsman is required to furnish 




the pattern-maker with a templet for laying out the exact tooth 
outline for certain gears, and let Fig. 60 represent the conditions. 
This pair of gears is not part of a set, simply designed to work 



T34 MECHANICAL DRAIVMG. 

together; note also that the gears are spur-gears and that the 
teeth are of the cycloidal system. 

To draw the teeth, draw the line of centers, A-B f properly 
locate the centers and draw the pitch-circles E-E and E r -E'\ 
draw the describing circles as shown, and of a diameter equal 
to three-eighths of the diameter of the respective pitch- circles. 
Now roll the describing- circle of the driver to the right and inside 
of the E'-E r pitch-circle and describe the hypocycloid i-h-i-j-k 
{Sect. 152); this curve forms the flank of the teeth for the driver. 
Again roll the same describing- circle to the right and this time 
on the outside of the E-E pitch-circle and describe the epicycloid 
\-l-m-n (Sect. 152); this curve forms the face of the teeth for 
the follower. Next roll the describing-circle of the follower to 
the left and inside of the E-E pitch- circle and describe the hypo- 
cycloid i-a-b-c-d; — this curve forms the flank of the teeth for the 
follower. Rolling the same describing- circle to the left again, 
and this time on the outside of the E f -E' pitch- circle, obtain 
the epicycloid i-e-j-g, which curve forms the face of the teeth for 
the driver. The tooth curves drawn, draw the addendum, 
•dedendum, and root- circles for the gears according to the usual 
proportions (Sect. 154). the circular pitch having been com- 
puted by formula 1. Sect. 155. Starting at the common pitch- 
point, 1, step off one- half of the circular pitch around the pitch- 
circles, and with a templet of the proper curve — an irregular 
curve properly marked — through these points draw in the outlines 
of the teeth as shown. 

Exact, Interchangeable Cycloidal. — Assume that the fol- 
lower of the above example is to form part of a set of gears, and 
let it be required to draw the exact tooth outline. As previously 
explained (Sect. 158), the diameter of the describing-circle is 
predetermined — found by substituting the known values in 
formula 1 and solving for D; the diameter of the rolling circle 
^equals one-half of D. Let Fig. 61, showing the follower in gear 
with the smallest gear of the set, represent the conditions. 

: i The describing-circles drawn, the method of procedure is iden- 
tical with that given for the non-interchangeable gear; it will 



GEARING. 



*ZS< 



be noted, however, that the hypocycloid obtained by rolling, 
the describing- circle inside the pitch-circle of the driver is a., 
straight line passing through the center of the pitch-circle, making; 
the flanks of the teeth of that gear to be radial lines. 




^FOLLOWER 



/ 



/ 



i / 



B 
Fig. 61. 



Exact Involute. — Let it be required to draw the above gears, 
with exact involute teeth, and let Fig. 62 be the diagram. To 
draw the teeth, draw the two pitch-circles as before, then draw 
the line of action, X-F, as shown, and the base circles, m-n and 
p-p, tangent to it. Next draw the involutes 0-1-2-3, etc -> anc ^ 
o'-2~3', etc., to the m-n and p-p base circles, respectively; these, 
curves form the face and part of the flank — that part between 
the pitch- circle and the base circle — of the teeth of the respective- 
gears, the remainder of the flanks being drawn as radial lines. 



136 



MECHANICAL DRAfVING. 



With the depth of the tooth defined, and the width of the tooth 
and space laid out on the pitch- circles, the tooth outline is drawn 
in as shown by means of templets to the involutes. 




Fig. 62. 

The construction of the exact tooth curve is both laborious 
and time-consuming; in fact so much so that there has been 
a number of methods evolved for approximating the curve. Of 
the various methods in use, that of approximating the tooth 
curve with circular arcs is the most widely used. The methods 
known as "Grant's Epicycloidal and Involute Odontographs" 
(see tables), the invention of George B. Grant, are taken, by 
permission of the author, from "Grant's Treatise on Gearing." 
They have nearly supplanted previous devices for the purpose 
in this country. 

The use of the tables is explained by the following examples: 
Approximate Cycloidal. — Fig. 1, Plate No. 11. Draw the 
pitch-, addendum-, dedendum-, and root- circles of the gears and 
lay off the width of tooth and space, as previously explained. 
With either the diametral or circular pitch, and the number of 
teeth known, to apply the table look in the column of teeth for 



GEARING. 



137 



GRANT'S TABLES FOR DRAWING GEAR-TEETH.* 

(Standard Interchangeable Series.) 

Grant's Involute Odontography 

Centers on Base Line. 





Divide by the 


Multiply by the 




Diametral Pitch. 


Circular Pitch. 


Teeth. 






Face 


Flank 


Face 


Flank 




Rad's. 


Rad's. 


Rad's. 


Rad's. 


10 


2.28 


.69 


•73 


.22 


11 


2.40 


.83 




.76 




.27 


12 


2.51 


.96 




.80 




•31 


13 


2.62 


I.09 




■83 




•34 


14 


2.72 


1.22 




.87 




•39 


15 


2.82 


1-34 




.90 




•43 


16 


2.92 


I.46 




■93 




47 


17 


3.02 


I.58 




.96 




•5o 


18 


3.12 


I.69 




•99 




•54 


19 


3.22 


1.79 


I 


03 




57 


20 


3-32 


I.89 


I 


06 




.60 


21 


3-4i 


I.98 


I 


09 




63 


22 


3-49 


2.o6 


I 


.11 




66 


23 


3-57 


2.15 


I 


13 




69 


24 


3- 6 4 


2.24 


I 


16 




7i 


25 


3-7i 


2-33 


I 


18 




74 


26 


3-78 


2.42 


1 


20 




77 


27 


3-8 5 


2.50 


I 


23 




80 


28 


3-92 


2-59 


I 


25 




82 


29 


3-99 


2.67 


I 


27 




85 


30 


4.06 


2.76 


I 


29 




88 


31 


4-i3 


2.85 


I 


3i 




9i 


32 


4.20 


2-93 


I 


34 




93 


33 


4.27 


3.01 


I 


36 




96 


34 


4-33 


3-°9 


I. 


38 




99 


35 


4.39 


3.16 


I 


39 


I. 


01 


36 


4-45 


3.23 


I 


4i 


I. 


03 


Interval 
37-40 










4.20 


1-34 


41-45 


4-63 


I.48 


46-51 


5.06 


1. 61 


52-60 


5-74 


I.83 


61-70 


6.52 


2.07 


7I-90 


7.72 


2.46 


91-120 


9.78 


3-ii 


1 21-180 


13.38 


4.26 


181-360 


21.62 


6.88 



* Taken, by permission, from "Grant's Treatise on Gearing.' 



138 



MECHANICAL DRAWING. 



Grant's Cycloidal Odontograph. 





For One Diametral Pitch. 


For One Inch Circular Pitch. 




For any other Pitch, Divide 


For any other Pitch, Multiply 


Number of Teeth 
in Gear. 


by that Pitch. 


by that Pitch. 


Faces. 


Flanks. 


Faces. 


Flanks. 


Exact. 


Intervals. 


RacVs. 


Dist. 


RacVs. 


Dist. R 


ad's. 


Dist. 


Rad's. 


Dist. 


IO 


10 


1.99 


.02 


- 8.00 


4.00 


62 


.01 


-2-55 


I 27 


II 


11 


2.00 


.04 


-11.05 


6.50 


63 


.01 


-3-34 


2.07 


12 


12 


2.01 


.06 


Infinity 


Infinity 


64 


.02 


Infinity 


Infinity 


13* 


13-14 


2.04 


.07 


14.50 


9-43 


■<>5 


.02 


4.60 


3.00 


15* 


15-16 


2. 10 


.09 


7.86 


3-46 


.67 


•°3 


2.50 


1. 10 


i7i 


17-18 


2. 14 


. 11 


6.13 


2. 20 


.68 


.04 


i-95 


.70 


20 


19-21 


2. 20 


•13 


5-i2 


i-57 


.70 


.04 


1.63 


•50 


23 


22-24 


2.26 


•15 


4-5° 


!-I3 


.72 


•°5 


i-43 


.36 


27 


25-29 


2 -33 


.16 


4. 10 


.96 


74 


•05 


1.30 


.29 


33 


3°~3 6 


2.40 


.19 


3.80 


.72 


76 


.06 


1.20 


•23 


42 


37-48 


2.48 


. 22 


3-5 2 


.63 


79 


.07 


1. 12 


.20 


58 


49-72 


2.60 


•25 


3-33 


•54 


83 


.08 


1.06 


•17 


97 


73-144 


2.83 


.28 


3-14 


.44 


90 


.09 


1. 00 


.14 


290 


I45-3 00 


2.92 


•31 


3.00 


.38 


93 


. 10 


•95 


. 12 


Infinity 


Rack 


2.96 


•34 


2.96 


•34 


94 


. 11 


•94 


. 11 



the number corresponding to the number of teeth of the gear to 
be drawn; this found, follow across to the column headed "Face, 
Dist." (diametral or circular pitch, as the case may be), and 
applying the instructions (to divide or to multiply) given in the 
table, lay off the length obtained as shown, and draw the circle 
of face centers. Going back to the column of teeth number in 
the table, find the corresponding "Rad's" number, and in accord- 
ance with the table instruction, compute the face radius; this 
found, with centers on the face radius circle, draw the face curve 
of the teeth. The circle of flank centers and flank radii are 
computed from the table in a similar manner and the flank 
curve of the teeth drawn as shown. 

Approximate Involute. — Fig. 2, Plate No. 11. The table for 
involute teeth is applied similarly to that for cycloidal teeth, with 
the exception that all centers are on the base circle. 

161. Rack and Pinion. Exact, Non-interchangeable Cy- 
cloidal. — Fig. 63. This is identical with the conditions given 
for spur-gearing (Sect. 160), the rack being a spur-gear of in- 



GEARING. 



139 



PLATE No. it. 



GEARING 

DIFFERENT SYSTEMS. 

Approximate method. 




1. CYCLOIDAL SYSTEM. 

(By Grant's Cycloidal Odontography 

EXAMPLES OF SPUR GEARS. 




2. INVOLUTE SYSTEM. 

(By Grant's Involute Odontography 



140 



MECHANICAL DRAWING. 



finite radius and its describing- circle a straight line E-E. By 
rolling the describing-circle of the pinion on the inside of the 




Fig. 64. 

pitch-circle, the hypocycloid P-M, forming the flanks of the 

pinion teeth, is obtained; by rolling the same circle along the 



GEARING. 



141 



pitch-line, the cycloid P-N, forming the faces of the rack teeth is 
obtained; by rolling the line E-E around the pitch-circle the in- 
volute, P-Oj forming the faces of the pinion teeth is described; 
the flanks of the rack teeth are drawn perpendicular to the pitch- 
line. 

Exact, Interchangeable Cycloidal. — Fig. 64 illustrates the ap- 




Fig. 65. 

plication of the uniform rolling circle of a set of gears, and the 
procedure is identical with that given in Sect. 160. 

Exact Involute. — Fig. 65. Here the tooth curve of the rack 




is a straight line; the base circle and involute P-M for the face 
of the teeth of the pinion are obtained in the usual manner and 
the teeth drawn as in Sect. 160. 

Approximate Cycloidal. — Fig. 66. Apply the cycloidal table 



142 



MECHANICAL DRAWING. 



as for spur-gears, the face and flank center circles for the rack 
becoming straight lines parallel with the pitch- lines. 

Approximate Involute. — Fig. 67. Draw straight lines for the 




Fig. 67. 

tooth curve of the rack teeth, and for the tooth curve of the pinion 
apply the involute table as for spur-gears, Sect. 160. 

A 




162. Internal Gears. Exact Cycloidal. — Fig. 68. To draw 
the teeth, draw the two pitch- circles tangent at the common pitch- 
point, P; draw the addendum- and root-circles of the usual pro- 



GEARING. 



J 43 



portions, and the describing-circles as shown. Rolling the 
describing-circle on the outside of the large pitch-circle generates 
the epicycloid P-E, which defines the flank curve for the teeth 




for the annular wheel; rolling the same describing-circle on the 
outside of the pitch-circle of the pinion generates the epicycloid 
'P-F, which defines the face curve for the teeth for the pinion. 




Fig. 70. 



Rolling the describing-circle on the inside of the pitch-circles gen- 
erates the hypocycloids P-G and P-PI, which form the face curve 
of the teeth for the wheel and the flank curve for the teeth of the 



144 



MECHANICAL DRAWING. 



pinion, respectively. The tooth curves defined, the teeth are 
drawn by means of a templet. 

Exact Involute. — Fig. 69. Draw the two pitch-circles and 
the line of action as shown; draw the addendum- circle of the 
pinion and the root- circle of the wheel as usual. The addendum- 
circle of the wheel is determined by the point F, and the root- 
circle of the pinion by the usual clearance. To draw the teeth, 
the base circles are drawn as for spur- gears, the involutes to 
them, P-E f and P-F f , described, and the teeth drawn as shown. 

Approximate Cycloidal. — Fig. 70. The pitch-, addendum-, and 
root-circles are drawn in the usual way and the cycloidal table 
applied as for spur-gears. 

Approximate Involute. — Fig. 71. The pitch- circles, the 




Fig. 71. 



addendum of the pinion, and the root-circle of the wheel are drawn 
in the usual way, and the addendum-circle of the wheel and the 
root-circle of the pinion, as in the exact example given above. 
These drawn, apply the involute table as for spur-gears. 



CHAPTER VHL 

COLOR WORK. 
TINTING. 

163. Introductory. — Tinting is the art of applying colors to 
drawings, and as a "touch of color" added to most things enhances 
their beauty, so does the art of tinting assist in the production of 
handsome drawings. The art is much used in the preparation 
of drawings for catalogue illustrations, this particular kind of 
work being a trade in itself and known as "wash drawing. " 
The art of tinting is, however, of some importance to the ordinary 
engineer- draughtsman, being much used by the architectural 
engineer for coloring plans and perspectives of buildings, and 
by others for expediting the drawing of sections, the sectioned 
part being colored as a substitute for cross-hatching. 

164. Outfit. — The outfit needed for the course as herein 
embodied is as follows: 

(1). Two small beakers for holding water. 

(2). Two sable or camel's-hair brushes, or, if preferred, one 
double-ended brush, one end for color, the other for clear water. 
The brush should be thick in the body, tapering rapidly to a 
fine point. 

(3). A nest of six cabinet saucers in which to mix the colors. 

(4). A bottle of library paste for mounting the paper. 

(5). A small hand sponge or rag with which to sponge the 
paper. 

(6). A six-inch square of ordinary fly- screening. 

(7). A tooth-brush or other small, stiff- bristled brush. 

(8). One-half pan (trade term) of Chinese white. 

(9). A small stick of Chinese or India black ink. 

145 



146 MECHANICAL DRAWING. 

The paper best adapted for tinting differs from a good drawing- 
paper in that it is comparatively rough of surface. 

165. Making a Stretch. — Since the tints are applied in a 
liquid form, there is more or less of a tendency for the paper to 
"blister," the moisture causing it to stretch and the corners being 
hxed, the paper blisters in proportion to the amount of the liquid 
applied. To meet this tendency, the paper is usually " stretched" 
on the board. This is done as follows: 

To make a stretch, first select the surface of the paper to 
receive the drawing, then lay the paper, with this side up, on 
a drawing-board and "square" the top edge of the paper with 
a T-square; next slide the square down for about \" and turn 
up this i" strip of paper against the edge of the T-square blade; 
then remove the square and fold the paper back; in this manner 
turn up and fold back a strip of about J" at each side of the sheet, 
turning the top side first, then one end, then the other, and lastly 
the bottom side; with the paper thus prepared, turn it over and 
with a sponge or rag apply a liberal wash of clear water, being 
careful to keep it off the upturned edges, and allow it to soak 
for two or three minutes; this expands the paper (should a very 
"tight" stretch be desired, the paper may be moistened on both 
sides; for the exercises of this course, moistening on the under- 
side will suffice) ; next turn the paper over on the drawing-board, 
squaring the last turned edge with a line drawn on the board, 
then rub the paper down — the moist surface will adhere to the 
board for a short time; now, apply a liberal coating of paste to 
the turned-up strips, being careful to keep it off the surface to 
be drawn upon, and taking them in the reverse order as turned 
up, fold them back and rub them down until perfect cohesion is 
obtained; when the paper is pasted on, and while the paste is 
yet moist, the paper should be drawn taut with the finger-tips; 
this gives an additional stretch to the sheet, which, being yet 
moist, is now permitted to dry, thus contracting the expanded 
sheet, and the pasted parts being fixed, the paper is stretched. 

166. Mixing the Colors. — To mix the stick ink, rub the stick 
with considerable pressure in a saucer containing a small quantity 



COLOR WORK. 147 

of water until the desired tint is obtained. To mix the Chinese 
white, moisten the tip of the cameFs-hair brush and apply it to 
the surface of the color, rubbing briskly and turning the brush 
until a quantity of the color is absorbed; then transfer the coloi 
to a saucer containing more or less water, according to the quan- 
tity and degree of color wanted. If the color is to be used in 
the ruling-pen, the pen may be charged directly from the brush- 
tip. 

167. Flat Wash. — A "flat wash" is the term applied to the 
application of a uniform tint. In applying the color, the brush 
should be well filled and a small "puddle" of color made on 
the surface to be colored; this puddle h washed over the surface, 
then picked up with a dry brush. This applies to fairly large 
surfaces; if the surface be small, the brush may contain but little 
color and the surface be "painted." 

The tints, if permitted to stand on the paper, will dry in a 
very short time, especially along the edges ; and when washed 
over and the sheet allowed to dry, they will appear streaked; for 
this reason it is important to keep all parts of the wash moving — 
the minimum speed is quickly ascertained in practice — until the 
wash is finished. If one cannot work with sufficient rapidity, 
the drying tendency may be minimized by first moistening the 
surface with clear water. Such a procedure is advantageous, 
also, as a vehicle for carrying the wash into intricate parts of 
the drawing, since the water can be applied slowly and with 
the necessary caution to preserve the lines; however, when so 
doing, care must be exercised to produce a uniform tint, as the 
added water will tend to lighten it. 

168. Shading. — There are a number of methods for shading 
with tints, principal among which are the following: 

1. To shade by means of flat tints, lay on a light tint flat 
wash for a short space, then soften off the edge with a clear, 
moist brush-end; when dry, begin as before, and this time carry 
the wash a little greater distance, then soften off the edge as 
above; in this manner apply a number of coatings, each succes- 
sive one covering all the others — a process which causes the 



148 MECHANICAL DRAWING. 

first applied wash to become darkest and grades from it to the 
last wash. The objection to this method is the great amount of 
time consumed in its application. 

2. A second method of applying shades is to mix the color 
to correspond to the deepest shade and make a puddle of this 
at the top of the surface; then pick up a quantity of clear water 
with the brush and add this to the color on the sheet, washing 
it down for a short distance; then add more water and wash it 
down, etc., adding clear water each time, thus thinning the tint 
and grading the wash from dark to light. This method requires 
much practice to determine the exact amount of water for a 
uniform grading of the tint. 

3. A third method is to begin as in the second method, 
with a puddle at the top, but this time thin the color off the 
sheet, in the saucers, then apply it. In these two methods it is 
important that a fair- sized puddle be maintained on the paper, 
thus insuring a more even thinning of the color and a uniform 
grading of the tint. Too much water will produce a streak, too 
little no perceptible change of tint. 

4. In this method first wash the surface to be shaded with a 
wash of clear water; do not apply enough water to cause it to 
stand on the surface, but just a quantity sufficient to cause the 
paper to " glisten" uniformly, and while yet wet apply the color — 
which should be quite dark — to the part which is to be darkest and 
draw the color from here to the high lights by streaking the sur- 
face with bands of color varying in width and spacing; to execute 
the shade, begin at the high light with a clean, moist brush- tip, 
and moving the brush back and forth at right angles to the direc- 
tion of advance, work through the bands of color to the darkest 
part. Should the shading be streaked or otherwise irregular 
while the surface is yet moist, begin again at the high light with a 
clean brush and again work through the shade. The advantage 
of the method is that as long as the surface is moist, the work 
may be gone over and bettered. 

In applying the bands of color, care should be exercised to 
have just the right quantity of the "iquid in the brush- t.'p; if too 



COLOR WORK, 149 

much is used, the color will run; if too little, the shade will be 
"pale." The color should be quite thick — heavy — and the brush 
should contain that quantity which remains after wiping the 
brush-tip a few times on the edge of the saucer. 

The clean brush should contain a quantity of water remaining 
after gently squeezing the brush-tip between the fingers — a fairly 
"dry" brush. If the brush contains too much water, the tint 
will be thinned too much and the shade will not be marked; if 
there be too little water, the brush will pick up the color and 
the shade will be streaked. 

5. When the surface is comparatively small, a fifth method 
may be used to advantage. In this, apply a small amount of the 
heavy tint, then with a clean, moist brush draw the color out, 
and as it is carried over the surface it will become thinned and 
the color graded from the original dark to light. The exact 
amount to first apply is a matter of practice. 

To minimize a tendency to dry too rapidly in the first, second, 
third, and fifth methods, clear water may be first applied, though 
the surface must be allowed to dry to a point where the " glisten' ' 
of the water disappears from the surface of the paper, else the 
color will follow the water and cannot be controlled. 



STIPPLING.* 

169. Introductory. — To "stipple" means to shade by means 
of dots. If the surface to be stippled is small, the work is usually 
done with a pen-point; if the surface is of some size, such a method 
is too time-consuming and difficult where good results are desired. 
For stippling such surfaces, there are several mechanical methods 
which may be used; that method to be followed in this course 
will be treated of as being typical of these processes. 

If a piece of ordinary wire fly-screening be held over a sheet 
of paper and a stiff brush — such as a tooth-brush — containing a 
liquid be brushed over the upper surface, it will throw dots of 

* Also called "Spatter Drawing." 



150 MECHANICAL DRAWING. 

the liquid onto the paper. This simple procedure is the method 
to be followed in executing the exercises in stippling. 

170. Method of Procedure. — For good results the paper 
should be stretched as for tinting, though if the amount of sur- 
face to be stippled is small and the degree of shade compara- 
tively light j the paper may be secured with thumb-tacks as in 
ordinary drawing. The color is mixed as for tinting; however, 
110 very light tints are used, as the light shade is here produced 
in a different manner. The figure to be "drawn" is executed 
on a sheet of fairly stiff paper — not the finished sheet — and is 
then prepared for stippling by cutting out the various surfaces; 
that is, make a templet for the figure, then lay this on the paper, 
matting out all other parts, and throw the dots on the exposed 
area. 

To stipple, dip the brush in the color, shake it until quite 
dry, then brush it across the screen. If the brush contains too 
inuch color the dots will not be clean-cut and often will run 
together and blur and blot. 

To shade lightly and uniformly, hold the screen some dis- 
tance away — three or four inches — from the paper; as the screen 
is moved closer to the paper the shading may yet be uniform, 
but will grow darker. Large surfaces are stippled by moving the 
screen about, and shades are intensified by holding the screen in 
one place and close to the paper. 



SKETCHING. 



*5* 



PLATE No. 12. 




PART II. 



CHAPTER IX. 

SKETCHING 

171. Introductory. — The "course in mechanical drawing" as 
embodied in these notes is divided into two parts: (1) sketching, 
and (2) mechanical drawing. The work in sketching is a prelim- 
inary to the mechanical execution of the copies given, and is 
intended to thoroughly acquaint the student with the funda- 
mentals of mechanical drawing. 

The sketches are to be drawn in pencil, on a specially ruled 
paper, with the aid of a compass, straight-edge, and scale. 

172. Sheet No. 1. — The first exercise, Plate No. 12, is an 
exercise in straight-lining and is to be copied, free-hand, exactly 
as set forth; the lettering is to be of the same size and style given, 
except where the words "Name" and "Date" occur the student 
is to print his name and the date of completing the sheet. 

The paper is to be placed as for writing, and with the hand 
in the natural relative position, the sheet is to be executed without 
either turning the paper or altering the position of the body; 
great care should be taken to make the lines of uniform weight 
and as straight and free from waves as possible. 

When completed, the sheet is to be submitted for inspection 
and acceptance before proceeding with the next exercise. 

173. Sheet No. 2. — Sheet No. 2, Plate No. 13, is an exercise 
for the training of the eye to recognize regular curves in balance — 
symmetry; it is a free-hand exercise and is to be drawn as follows: 

Locate the center lines and work to them by checking the 
cross lines every half inch or less, and measure the distance of 

1 5 2 



SKETCHING. 



*53 



PLATE No. 13. 




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154 MECHANICAL DRAWING, 

the points at which the curve of the copy crosses these cross lines, 
then lay these distances off (by counting spaces) on the corre- 
sponding cross line of the drawing, mark the points, and draw 
the curve through these points, making the lines very light until 
satisfactory, then trace them until distinct. 

174. Sheet No. 3. — Sheet No. 3 is an exercise in the free-hand 
construction of letters and figures. As a preliminary ' for this 
sheet, Chapter II should be carefully digested. 

To draw the sheet, use Plate No. 3 as a copy and construct 
the following alphabets: 

1. Alphabet No. 1, making the letters and figures J" high. 
Note the copy is the square alphabet. 

2. Draw alphabet No. 1, \" high. 

3. Draw alphabet No. 3, \" high. 

4. Draw alphabet No. 2, the guide-lines to be }" apart. 

5. Draw alphabet No. 4, the guide-lines to be: center spacer 
J"; the space above and below this = T 1 F // . 

6. Draw a number of miscellaneous fractions proportioned 
in accordance with copy No. 5. 

Reserve a space 2 ,r X 3" in the lower right-hand corner of 
the sheet for the following title : * 

SHEET NO. 3. 
Letter-sheet No. I. 

Name. Date. 

Note. — Begin one space from the top of the sheet and one 
space in from the left border line, and allow one space between 
letters and two spaces between rows. 

When complete, submit the sheet for inspection. 

175. Sheet No. 4. — Use Plate No. 3 as a copy and draw two 
copies of No. 6 — entire lower half of the plate; the student is 
to make a choice of size, spacing, and balance for the lettering, and 
is to space the following title in the usual letter space: 

* In lettering this and all other sheets, and for all lettering, use the styles of 
letters given in Chapter II and not the type letters appearing on the plates. 



SKETCHING. 155 

SHEET NO. 4. 
Letter-sheet No. 2. 

Name. Date. 

176. Sheet No. 5.— Sheet No. 5, Plate No. 14, is a mechanical 
drawing, front and right elevations and bottom view, of a lathe 
detail (Fig. 70) , and is to be executed exactly like the copy, using 
the compass and straight-edge. 




THE CETAIL 

Fig. 70. 

177. Sheets Nos. 6 to 20, Inclusive. — These sheets are to be 
scale drawings from models, such as could be taken into a shop 
and with the drawing as a guide the piece could be produced. 

In these drawings care should be exercised to produce a 
well-balanced sheet, to place the views so as to bear the proper 
relation to one another, thus rendering the sheet easily legible, 
and to give all necessary dimensions and notes. Reserve the 
standard letter space — 2 ,, X3 ,/ — for a title. 

To illustrate the character of these fifteen drawings, the fol- 
lowing examples are given, and in the absence of models from 
which to draw, they may be used as a copy; the intention of 
this part of the course, however, is to give the student practice 



156 



MECHANICAL DRAWING. 



PLATE No. 14. 



Form ,D 



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SKETCHING. 157 

in original drawing, and to this end the following models, which 
are universally obtainable, are named as being representative: 

Hammers, Bicycle parts, 

Wrenches, Stove parts, 

Pipe-fittings, Ink-bottles, etc* 

Valves, Spools, 

Machine parts, Boxes. 

The notes on these drawings illustrate a common shop prac- 
tice, that of numbering the pattern for an object, so that should 
duplicates of the piece be wanted at any time, in place of supply- 
ing the shop with a new drawing, one has but to say "Use pattern 
No. — ." The notes as to the number wanted, finish, etc., are 
in accordance with Sect. 51. 

The name of the piece given in the letter space represents 
real practice ; for the course the title of the sheet may be simply 
the consecutive "Sheet No. — ." 

178. Sheet No. 21. — Draw the projections of a 2" cube with 
a 1" square hole through its center, and assume the cube to rest on 
the horizontal plane. (Reference, Sect. 75.) 

Use Fig. 3, Plate No. 7, as a copy, with the following dimen- 
sions: X and Y = standard sheet, 7"Xo/'; A = \\", 5 = 2§", 
C = 2j", £> = 2f", £ = if", F=i}". Execute a full-sized draw- 
ing, drawing the figures as numbered. Omit all dimension 
lines and letter the sheet as in Fig. 21. 

179. Sheet No. 22. — Exe:ute a full-sized drawing of the pro- 
jections of a blank, hexagonal nut, Fig. 17, the nut to rest on the 
horizontal plane. (Reference, Sect. 76.) 

Draw the figures in the order numbered, using the following 
dimensions: ^ = ij", J3 = iJ", C (the distance of the center line 
from the left border) = 2§ " ; ground line to be in center of sheet. 
Omit all dimensions. 

180. Sheet No. 23. — Execute a full-sized, well-balanced draw- 
ing of Fig. 20, completing the projection B; all working lines to 
be very light and to show on the finished drawing. Omit all 
dimensions. (Reference, Sect. 77.) 



158 



MECHANICAL DRAWING. 



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MECHANICAL DRAWING, 



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SKETCHING. 



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PLATE No. 18. 




162 



MECHANICAL DRAWING. 



PLATE No. 19. 




SKETCHING 



163 



PLATE No. 20. 




164 



MECHANICAL DRAWING. 



PLATE No. 21. 





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MECHANICAL DRAWING. 



PLATE No. 25. 




SKETCHING. 



169 



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17° MECHANICAL DRAIVING. 

181. Sheet No. 24. — Execute a full-sized drawing of Fig. 21, 
drawing the figures in the order numbered; show all working 
lines and omit all dimensions. (Reference, Sect. 78.) 

182. Sheet No. 25. — Execute a full-sized drawing of Pro- 
jection No. 5, Fig. 24. (Reference, Sect. 79.) 

183. Sheet No. 26, Plate No. 8. — A. Execute a full-sized 
drawing of Fig. 5. (Reference, Sect. 80.) 

B. Draw the developments of the two cylinders (Fig. 4), 
the sheet to be well balanced and all working lines to be shown. 

184. Sheet No. 27, Plate No. 9. — A. Execute a full-sized 
drawing of Fig. 5. (Reference, Sect. 81.) 

B. Draw the developments of the cylinder and of the cone. 
(Figs. 2 and 4.) 

185. Sheet No. 28. — A. Execute a full-sized drawing of Fig. 25* 
(Reference, Sect. 82.) 

B. Draw the developments of the cylinders, cutting cylinder A 
along the element 4-4 and cylinder B along the element 1-7 (out- 
side element). 

186. Sheet No. 29. — Execute a full-sized drawing of Fig. 27, 
and let it be required to construct a shade with twelve points 
around the bottom as indicated by the dotted lines; allow }" 
lap. (Reference, Sect. 83.) 

187. Sheet No. 30. — Execute an isometric drawing of some 
simple piece of mechanism, drawing from the model; give all 
dimensions and balance the drawing; the title space to contain 
the following: 

SHEET NO. 30. 

Isometric Drawing No. I. 
From Model. 

Name. Date. 

188. Sheet No. 31. — Execute an isometric drawing of some 
simple piece of mechanism, drawing from the mechanical draw- 
ing of the object. (Select drawing from Sheets Nos. 6 to 20, 
inclusive.) Give all dimensions; letter as above. 

189. Sheet No. 32. — Execute an original isometric drawing 



SKETCHING. 17 1 

in accordance with either Sheet No. 30 or 31, omit all dimensions* 
and shade the drawing. 

190. Sheet No. 33. — Execute an original assembled mechan- 
ical drawing of some fairly simple machine, giving all dimen- 
sions and notes necessary on such drawings. (Read Sect. 51.) 

191. Sheets Nos. 34 to 40, Inclusive.— These sheets are what 
will be known as " working-sketches. " They are to be free-hand, 
detail, and assembled drawings drawn from the various machines 
in the different laboratories, and are later to be reproduced as 
pen-and-ink scale drawings, some of them to be on paper and 
others to be drawn on tracing- cloth. These sketches must be 
complete, not with reference to the mere drawing alone, but with 
reference to dimensions, notes, etc.; in preparing his sketch, 
the student is to assume he is never again to see the object and 
must be able, months hence, to construct a drawing from his 
sketch such that the thing could be reproduced with the draw- 
ing as the only " guide. " 



CHAPTER X. 

THE MECHANICAL EXECUTION OF DRAWINGS. 

192. Introductory. — Having completed the course in sketch- 
ing, the student should have a good working knowledge of the 
underlying principles of mechanical drawing and be prepared 
to take up the study of drawing- tools and the mechanical con- 
struction of practical drawings. With this end in view, Plates 
Nos. 27 to 57, inclusive, are given as examples in drawing, calcu- 
lated to further the student's knowledge of the subject, to be his 
copy for the manual use of instruments, and being representative 
sheets of every-day practice, to afford him a field for acquiring 
that proficiency of execution and construction which is required of 
the practical draughtsman. 

In the execution of these copies, the plates are to be accurately 
reproduced in accordance with the instructions given for each 
sheet, and with such dispatch as is consistent with clean-cut, 
neatly finished work. The tools required for the work are such 
as is given in the "Draughtsman's Outfit," page 85. 

193. Sheet No. 1, Plate No. 27. — The sheet of paper given 
for this and for all of the other exercises is the standard g¥'X 12" 
sheet and is to finish 9 // Xi2 // ; this allows a waste of J" to be 
apportioned, J" at the top and \" at the bottom of the sheet to be 
used as "try" paper(to try the ruling-pen, etc., on), and when cut 
away (when the sheet is completed) removes the thumb-tack 
holes. 

To secure the paper to the drawing-board (Fig. 53) place the 
paper approximately in the center of the board — the narrow 
way — and 3" or 4" nearer the left side of the board (if right- 
handed) than the right side; now place the T-square on th? 

172 



MECHANICAL EXECUTION OF DRAWINGS. 



173 



PLATE N<X 27. 




174 MECHANICAL DRAWING. 

board as shown, hold the paper with the right hand and with the 
left hand on the T-square head move the square towards the top 
of the board until the top edges of the square and paper coincide, 
turning the paper as is necessary to " square" it with the square; 
with the paper thus "squared," remove the square and place a 
thumb-tack in the upper left-hand corner of the sheet; then keep- 
ing the paper square, run one hand — with considerable pressure 
—along the top edge of the paper, stretching it to the right-hand 
corner, and tack it; these two corners secured, stretch the paper 
from the center to the two lower corners and tack them. 

The paper secured, with the architect's scale lay off the 
S^Xn" border and mark the cutting lines; now with the T- 
square for horizontal lines, and the T-square and either triangle 
for vertical lines, draw the lines through these points which form 
the 8"Xn" inclosed space to receive the drawing, then lay out 
and draw the 2"X3" letter space. 

Working to the dimensions given, lay off a top and bottom, 
line for the row of lines and pencil them in, making all of the 
lines light, full lines, and when satisfactorily spaced, ink them, 
showing the different lines. 

For the second row of figures, locate the centers for the circles^, 
and with the compass set with the proper radius, the circles may 
be inked without any preliminary penciling. 

The next two rows are to be penciled in as dimensioned, and 
then inked in Much care is necessary here to produce smooth 
lines and evenly undulating curves. 

The bottom row on the plate is given to introduce the shade 
line — "back lining" drawings. The small arrows represent the 
projection of the rays of light, which are assumed to be parallel 
and to strike the plane of the paper at an angle of 45 . Con- 
sidering the hollo vv, rectangular figure on the left, it is evident 
that the top and left-hand lines of the outside of the figure will 
be in the light — illuminated — and should be drawn as light lines; 
also that the bottom and right-hand lines of the outside of the 
figure cut off the light and represent faces of the object which 
are in the shadow, and should be drawn as heavy or shade lines. 



MECHANICAL EXECUTION OF DRAWINGS. 



i7S 



It should be noted that the shading on the interior of the draw- 
ing is the reverse of that on the exterior. 

To shade the circular drawing as "called for" by the arrows, 
draw the diameter E-F with the 45 triangle, then draw the 
diameter G-H at 90 with E-F and 45 with A-B, and cutting 
E-F at a point about -gV" to T V" from the center; now with the 
center defined b the intersection of A-B and C-D, and the 
proper radius, describe the circles, and to shade them, take a 
new center — the intersection of E-F and G-H — and with the 
same radius used for the circles (see Fig. 71), shade the larger 





Fig. 71. 

one on the lower right-hand side and the smaller circle od th? 
upper left-hand side. 

The right-hand figure of the row is to be shaded liKe the 
copy. 

The drawings completed, draw top and bottom guide-line? 
for the title lettering, the top row to be \" high, the middle row, 
initial letters iV' high, other letters J" high; name and date- 
initial letters J" high, other letters 3V' high; to be spaced approxi- 
mately like the copy; pencil in the letters until satisfactory, then 
ink them in free-hmi. 

When completed, submit the sheet for inspection and accept- 
ance befDre taking up Sheet No. 2. 



170 MECHANICAL DRAWING. 

194. Sheet No. 2, Plate No. 28. — This is an exercise for a test in 
accuracy of manipulating the compass and bow-pen, and is to be 
first constructed in pencil, then inked in. To draw the sheet, begin 
with the large central figure by locating the horizontal and vertical 
center lines intersecting at the center of the sheet; with this point 
as a center and a 3" radius, describe the 6" circle; then with the 
same center, describe the 3" circle, and with the points in which 
it intersects the two diameters as centers, and the same radius 
used for the 3" circle, draw the four other circles, then draw 
the exterior arcs as indicated. 

To draw the three small designs, locate the center lines and 
draw the 2" and i 3 / 10 " circles; then with the T-square and 45 
triangle draw the two diagonal center lines, and with the eight 
points in which the i 3 /ie" circle intersects the four center lines as 
centers and a radius of iV 16 " describe the eight circular arcs as 
shown. 

195. Sheet No. 3, Plate No. 29. — This sheet is given as an 
exercise for practice in ruling straight lines and to acquaint 
the student with the standard cross-hatchings most used in 

drawing. 

To draw the sheet, pencil in the fifteen rectangles according 
to the dimensions and proceed as follows: For cast iron, from the 
upper left-hand corner of the rectangle draw a 45 line to the 
right and on it lay off points Vae" apart; with the T-square and 
45 triangle draw the ruling through these points and when 
satisfactory, ink it in, inking the border last; this applies to all of 
the fifteen spaces, i.e., ink the border last. 

For wrought iron, draw a 45 spacing line as for cast iron, lay 
off 7 32 " lengths and draw (in ink) the light line; then, using the 
eye for the spacing, draw a heavy line about l / n " below each 

light line. 

For steel, use the eye for the spacing and draw two fine lines 
about 732" apart, and space the pairs of lines about Vie" apart, 
inking them in without any preliminary penciling. 

For brass and lead, use the eye for the spacing (about Vie") 
and ink directly. 



MECHANICAL EXECUTION OF DRAWINGS. 



177 



PLATE No. 28. 




178 MECHANICAL DRAWING. 

For copper, draw the pencil-lines denning the blank spaces 
and ink directly, approximating a y i6 " space between lines. 

Aluminum and wires are to be inked directly, with approxi- 
mate spacings. 

Brick and stone are to be accurately blocked out in pencil, 
inked in, then the cross-hatching approximated. 

Sand is made free-hand with a writing-pen, dotted in in ink 
directly. 

Earth is first ruled in ink, then "touched up," free-hand, 
with a writing-pen. 

Water is an approximate ruling, and glass is free-hand pen 
work. 

The spacing given, about 1 / 1 ", applies to spaces to be cross- 
hatched of about the size of the rectangles of the plate; if the 
space to be cross-hatched be greater than this, the space between 
lines should be increased proportionally; if smaller, it should be 
decreased. 

196. Sheet No. 4, Plate No. 30. — This is to be a free-hand 
exercise, the letters to be " single- line " letters. To draw the 
sheet, begin with the upper-case letters, square type, and draw 
the top and bottom guide-lines and pencil in the alphabet, omit- 
ting the numbers and arrows illustrating the number and direction 
of the strokes; when the letters are properly penciled, ink them 
in, then proceed with the slanted alphabet, using the top and 
bottom guide-lines and inking in directly. Complete the upper- 
case letters, using only top and bottom guide-lines and inking 
directly. 

Execute the first row of the lower-case letters, first in pencil, 
omitting arrows and numbers, then ink them in; proceeding as 
for the upper-case letters, complete the alphabets. 

Put on the headings and title last, then erase all construction 
lines. 

Omit all dimensions. 

197. Sheet No. 5, Plate No. 31. — Fig. 1 is an elevation draw- 
ing of the "business end" of a twist drill and is a practical exam- 
ple of the helix. To draw the figure, locate the center line, 



MECHANICAL EXECUTION OF DRAWINGS. 



179 



PLATE No. 29. 


























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MECHANICAL DRAWING. 



describe the semicircle 1-2-3, ... 7 and divide it into six equal 
arcs, then draw the rectangular outline and copy the lines of the 
plate, using the small irregular curve as is suggested by the dotted 
lines; the curve at the top, representing a broken end, is drawn 
free-hand. When the figure is accurately drawn in pencil, ink 
in the drawing by inking the curved lines first ; to do this, use the 
ruling-pen and curve, holding the pen in a vertical position, as 
shown in Fig. 72, and turning the pen with the curve, thus keeping 
the edges of the nibs parallel at all points with the guide. 




Fig. 72. 



Fig. 2 illustrates two methods of drawing ellipses when the 
axes are at right angles. First method: Locate the center lines 
and draw the two circles; divide the large circle into twenty-four 
equal parts (this can be done by means of the T-square and both 
triangles) and draw a radial line to each point of division. To 
locate points on the ellipse, consider the radial line 8-C; from 
the point in which this cuts the large circle, drop the perpen- 
dicular 8-4, and from the point in which it (&-C) cuts the small 
circle, draw the horizontal 8-8 — the intersection of these two 
lines is a point on the ellipse; the other twenty- three points of 
the curve are obtained in a similar manner. The points — the 
locus of the curve — obtained, use the irregular curve as is suggested 



MECHANICAL EXECUTION OF DRAWINGS. 



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1 82 MECHANICAL DRAWING. 

by the plate (note the lap of the consecutive positions) and pencil 
in the ellipse. 

Second method: Secure a strip of heavy paper one edge of 
which is a straight edge, and on this edge lay off from some point, 
as A, a length A-C equal to the semi-major axis of the ellipse, then 
trom the same point (-4) lay off a second length, A-B, equal to 
B-C, the semi- minor axis of the ellipse; now with the point C 
on the minor axis (extended) and the point B on the major axis 
rotate the strip of paper (the point C moving back and forth along 
the minor axis, and the point B moving up and down along the 
major axis) about the center, C, and dot the travel of the point A ; 
the curve is then drawn through these points. 

After both curve) have been accurately constructed in pencil, 
trace them in ink with the ruling-pen and curve. 

Fig. 3. This figure illustrates a method of constructing any 
curve. To construct the curve, locate the center line, draw 
horizontal lines every J", lay off on these the lengths given in 
the copy, and with the curve pencil in the drawing, and when 
satisfactory ink it in. 

Fig. 4 illustrates a method of constructing an ellipse when 
the axes are not at right angles. To construct the ellipse, draw 
the rhombus A-B-C-D and the major (n-ii) and minor (X-Y) 
axis of the curve; divide the semi-major axis (0-11) into a num- 
ber of equal parts, and the line D-n into the same number of 
equal parts; draw radial lines from point X through the points 
of division on the major axis, and radial lines from point Y 
through the points of division on line D-11; the intersections 
of the lines drawn to the same numbered point are the points 
through which the ellipse is drawn. 

The plate illustrates the locating of points for but one-quarter 
of the curve; points for the other three-quarters are located in a 
similar manner. 

To finish the sheet ink in the two construction circles for the 
ellipses, also the rhombus; omit all other construction lines. 
Give all dimensions, except those given for balancing the sheet, 
and center lines. (Do not ink in the outline of the French curve.) 

198. Sheet No. 6, Plate No. 32. — This sheet is an example 



MECHANICAL EXECUTION OF DRAWINGS. 



183 



PLATE No. 31. 





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184 



MECHANICAL DRAMNG. 



of structural iron draughting, and is to be first constructed in 
pencil, to a scale of i" = i', without any letters or figures, and 
submitted for inspection, then inked in, and the letters and figures 
drawn last. Space the lettering of the title so as to add the line 

"Scale.... 



i" = i\" 




Fig. 73 



199. Sheet No. 7, Plate No. 33. — This sheet is given to 
illustrate methods of representing screw-threads, and as a guide 
for drawing bolts and nuts. Fig. 1 represents a hexagonal-headed 
bolt and nut; to draw the figure, locate the center line, and with 
dimension D — the diameter of the bolt — equal to one inch, cal- 
culate all other dimensions and proceed as follows: First draw 
the end view, circumscribing the hexagon about the large circle 
with the T-square and 6o° triangle, then project the side view of 
the nut and the body of the bolt. To draw the screw-threads, 
begin on the right-hand side of the outline of the bolt, at a point 
as dimensioned, and on the continuation of this line lay off 
J" divisions, and with the T-square and 30 triangle draw the 
V's on this side; now on the left-hand outline of the bolt, begin- 
ning at a point 2 T V" from the bolt- head— r *" nearer than on the 
right side — lay off a number of J" divisions, and draw the V's on 
this side; to end the bolt, with a center at the point of the last 
V (right side) and a radius equal to the diameter of the bolt (D), 
strike an arc intersecting the center line (see Fig. 2) and with this 
point as a new center and the same radius, strike the arc of the 
end of the bolt; finish by connecting the tops and bottoms of each 
row of V's. 

The drawing represents a right-hand V thread, an outside 



MECHANICAL EXECUTION OF DRAWINGS. 



1*5 



PLATE No. 32. 




1 86 MECHANICAL DRAWING. 

thread on the bolt, and an inside thread in the upper half of the 
nut; note the direction of the inclination of the threads, also 
that the top of a V on one side of the bolt is directly opposite the 
bottom of a V on the opposite side of the bolt ; that is, the nut 
advances one-half thread in traveling half way around the bolt. 

The pitch of a thread is the distance from the point of one 
thread to the point of the next, in the drawing, shown as J", and 
spoken of as "eight pitch." The figure illustrates a convenient 
method of representing all V threads, though not always a true 
representation, as there are various kinds of threads, as single, 
double, triple, etc.; in such cases a note relative thereto should 
be added to the drawing. 

In addition to the above, there are a number of types of threads, 
as the American and European standard forms of V threads, 
square threads, buttress threads, and others, an elaborate expo- 
sition of which is reserved for the work in elementary design; 
however, the simple V thread as given is conventional for all 
forms of V threads, unless, of course, an accurate representation 
is desired, and is rendered specific by the addition of a note, 
as "U. S. standard V, double, 4 pitch." 

The V thread is always drawn showing a 6o° V, using the 
T-square and 6o° triangle. 

Fig. 2 represents a square-headed bolt and nut, showing a 
left-hand V thread. The end view is drawn first and the re- 
mainder of the figure constructed substantially the same as in 
Fig. 1. 

Fig. 3 represents a chamfered, hexagonal-headed, square- 
threaded bolt. To draw the figure, locate the center line, draw 
the end view, then project the head of the bolt and proceed with 
the thread, which is analogous with the V thread. 

The drawing of this figure is to be shade-lined in accordance 
with the other drawings of the sheet; the "shade" should be 
drawn outside of the outline dimensions. 

The conventions given for representing screw-threads are 
at best tedious and difficult, especially so for threads of small 
diameter. To further expedite the work, the conventions illus- 



MECHANICAL EXECUTION Oh DRAWINGS. 



187 



PLATE No. 33. 




i88 



MECHANICAL DRAWING. 



trated in Fig. 4 are often adopted, the end A representing a 
V thread, and the end B a square thread, the inclination of the 
lines being slightly out of a right angle with the side lines and 
all parallel. 

200. Sheet No. 8, Plate No. 34. — This sheet is given as a 
guide for drawing block- letters and as an exercise in free-hand 
lettering. The block-letters are drawn with instruments in 
accordance with the directions given on the sheet; the remainder 
of the plate is to be drawn by first ruling top and bottom guide- 
lines in pencil, then executing the lettering free-hand with the 
writing-pen without any preliminary lettering in pencil. The 
letters are to be of the following dimensions: Captions, initial 
letter to be T V high, other letters J" high; descriptive matter, 
initial letters, J" high, other letters /g" high; space between 
lines sV* 

In the free-hand work great care must be exercised to make 
the letters of uniform height and spacing, the words compact, and 
the lines of uniform weight. No guide or construction lines are 
to show on the finished sheet. 

201. Sheet No. 9, Plate No. 35. — This plate is a working- 




THE FRAME 

drawing of a simple blue-printing frame of a size to print the 
standard sheet of this course; i.e., o/'X^' 



jt 



MECHANICAL EXECUTION OF DRAWINGS. 



189 



PLATE No. 34. 




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190 



MECHANICAL DRAWING. 



To draw the sheet, locate the center lines of the front view 
(the large rectangular figure) and working to these, copy the 
drawing and when complete project the side views. 

202. Sheet No. 10, Plate No. 36. — This plate is given in the 
nature of a problem in drawing, illustrating the relation of the 
different views of an object; the "problem" is to construct a 
plan drawing of the object, working from the lines and dimen- 




THE SUPPORT 
Fig. 75. 



sions presented by the two elevations. The drawing is to be a 
scale drawing, one-half size, and a note relative thereto inserted 
in the title space. 

To draw the sheet, construct the drawing on the right hand — ■ 
the right side elevation — first, then project the front elevation. 



MECHANICAL EXECUTION OF DRAWINGS. 



191 



PLATE No. 35. 




I9 2 



MECHANICAL DRAWING. 



203. Sheet No. 11, Plate No. 37. — This plate presents a 
working drawing of a locomotive throttle stuffing-box. To draw 
the sheet, locate the center lines, construct the front- elevation 




THE BOX 
Fig. 76. 

drawing first (the figure on the left of the plate), then project the 
side elevation. The scale is to be one-half size. 

204. Sheet No. 12, Plate No. 38. — This exercise is an example 



Threaded for tumbuckle 




k 




ONE OF THE FORCINGS, A LATERAL ROD 

Fig. 7Z 

of bridge drawing. The sheet is to be drawn to a scale of ij" 

(j- size); all lettering to be free-hand. 



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MECHANICAL EXECUTION OF DRAWINGS. 



J 93 



PLATE No. 36. 





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MECHANICAL DRAWING. 



PLATE No. 37. 







MECHANICAL EXECUTION OF DRAWINGS, 



195 



PLATE No. 38. 



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196 



MECHANICAL DRAWING. 



205. Sheet No. 13, Plate No. 39.— This sheet is a drawing 
for the shop, and is to be drawn to a scale of 3" = i', or \ size, 
and a " scale note" added to the title space. 




THE HEAD 
Fig. 78. 

206. Sheet No. 14, Plate No. 40. — A second problem in 
drawing, similar to that of Sheet No. 10, is here introduced. 
Working with the plan and elevation drawings and to center lines, 



MECHANICAL EXECUTION OF DRAWINGS. 



197 



PLATE No. 39. 






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MECHANICAL DRAWING. 



construct a right end view drawing of the stub, to a scale of 



4" = i'. 




<^3' 



THE STUB 
Fig. 79. 



In addition to the above problem, the student is to shade 
line — back line — the entire sheet. 

207. Sheet No. 15, Plate No. 41. — This sheet is a detail sheet, 
detailing four fittings for the head stock of a wood- turning lathe. 




Head-stock Cap 



Nut for Bearings 



LATHE DETAILS 
Fig. 80 



Qn£ o.f the Be arings 



The student should note the arrangement and balance of the 
sheet. 



MECHANICAL EXECUTION OF DRAIVINGS. 



199 



PLATE No. 40. 





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MECHANICAL DRAWING. 



The cross-hatched portions of the top row of figures illus- 
trate the fit of the bearings and the use of the pin which keeps 
them (the bearings) from turning. 

208. Sheet No. 16, Plate No. 42.— This sheet is an exercise 
in free-hand lettering. The student is to decide the size of letters, 
spacings, and balance of the sheet. 

209. Sheet No. 17, Plate No. 43.— An assembled shop drawing 




THE JOINT 

Fig. 81 



of a universal joint. Construct a full-size drawing and shade 
the end view. 

210. Sheet No. 18, Plate No. 44.— This sheet introduces a 
third problem in drawing. The sheet is to be drawn to a scale 
of 3" = i', and in the two elevations show a half section taken on 
the line A-B-C of the plan drawing — the plan drawing to be 
drawn like the copy. (See Fig. 82.) 

211. Sheet No. 19, Plate No. 45. — This sheet is an exercise 
for practice in line shading, an operation for which the following 
general rules may be found useful: 

1. A surface which is parallel to the plane of projection and 
in the light is uniformly covered with light; a light line uniformly 
.spaced (1 and 2) illustrates the ruling for such a surface. 

2. A surface which is parallel to the plane of projection and 



MECHANICAL EXECUTION OF DRAWINGS. 



20I 



PLATE No. 41. 




202 



MECHANICAL DRAWING. 



PLATE No. 42. 



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203 



PLATE No. 43. 




204 



MECHANICAL DRAWING. 



PLATE No. 44. 



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MECHANICAL EXECUTION OF DRAWINGS. 



205 



PLATE No. 45. 




2o6 



MECHANICAL DRAWING. 



in the shadow is uniformly dark and is illustrated by uniform 
ruling of heavy lines closely spaced. 




THE BLOCK, SECTIONED. 
Fig. 82. 



3. Of two or more surfaces which are parallel to the plane 
of projection, the surface nearest to the plane is the lightest and 
the one most remote the darkest. 

4. A surface which is inclined to the plane of projection and 
in the light becomes lighter as it approaches. 

5. A surface which is inclined to the plane of projection and 
in the shadow is dark nearest the plane and becomes lighter as 
it recedes. 

Figs. 1 and 2 show a uniform line uniformly spaced; 3 and 
4 show a uniform space, variable line, drawn from light to heavy 
— "drawn in"; 5 and 6 show the same " drawn out." 

Figs. 7 to 12, inclusive, illustrate conventional shadings for 
representing cylindrical surfaces; 7 and 8 show a uniform line, 
variable space; 9 a uniform space and variable line, and Figs- 
10, 11, and 12 variable space and line. 

Fig. 13 is a uniform line uniformly spaced, used to represent 



MECHANICAL EXECUTION OF DRAWINGS. 



207 



PLATE No. 46. 



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208 MECHANICAL DRAWING. 

flat discs, the ends of cylinders, etc., when parallel to the plane 
of projection. 

Fig. 14 is a uniform line with variable spacing, and Fig. 15 a 
variable space and line, and illustrate conventions for represent- 
ing spheres. 

212. Sheet No. 20, Plate No. 46. — The sheet is a free-hand 
sheet; the student is to decide the size of letter, space, balance 
etc. ("Schenectady No. 2" is the name of Purdue's present 
experimental locomotive.) 

213. Sheet No. 21, Plate No. 47. — Fig. 1 represents a sphere; 
Fig. 2 a concave surface, the interior of a hollow cylinder; Fig. 3 
represents one-half of a hexagonal prism; Fig. 4 a ring which 
is circular in section. To shade the view on the left, draw a 
number of fine lines parallel to the sides and "touch up" be- 
tween them, free-hand, with an etching-pen. 

Fig. 5 illustrates two shadings for screw-threads, the upper 
end being shaded with fine, ruling-pen lines and "touched 
up," free-hand; the lower end is shaded with the writing-pen 
alone. 

Figs. 6 and 7 represent cylindrical surfaces, Fig. 6 illustrat- 
ing the "treatment" of double-curved surfaces and Fig. 7 the 
contrast between inside and outside curves, concave and convex 
surfaces, respectively. 

Fig. 8 represents a number of flat surfaces parallel with the 
plane of projection, as an elevation of a flight of steps, the several 
heavy lines at the top of each rise, indicating the shadow of the 
nose of the step tread. 

214. Sheet No. 22, Plate No. 48. — This sheet is given as a pre- 
liminary to the drawing of gear-teeth, and is also an excellent 
exercise for practice in the use of the irregular curve; the 
chapter on gearing should be carefully read before beginning the 
drawing. 

The sheet is to be a full-size drawing to the dimensions 
given, and is to be executed in accordance with Sect. 152. All 
lines, letters, and figures of the copy are to be shown on the fin- 
ished sheet; omit all dimensions. 



MECHANICAL EXECUTION OF DRAIVINGS. 



209 



PLATE No. 47. 




2IO MECHANICAL DRAWING. 

215. Sheet No. 23, Plate No. 49. — Here is presented a first 
exercise in the construction of gear-teeth. The sheet is to be a 
full-size drawing, and is to be executed in accordance with Sect. 
160. The finished sheet is to show all lines, letters, and figures, 
except the dimension lines, given in the copy. 

216. Sheet No. 24, Plate No. 50. — This sheet is a second 
exercise in the construction of gear- teeth, and is to be drawn 
full size, in accordance with Sect. 161 ; the finished sheet is to 
appear like the copy, without the dimensions. 

217. Sheet No. 25, Plate No. 51. — The sheet is another 
exercise in the construction of gear-teeth, and is to be a full-size 
drawing, to be executed in accordance with Sect. 162; the sheet 
is to be finished the same as the other sheets of the set. 

218. Sheet No. 26, Plate No. 52. — Here is presented a prac- 
tical example of the construction of gear-teeth, the drawing 
being a front and side elevation drawing of a pair of involute 
gears. The sheet is to be a full-size drawing, and is to be exe- 
cuted in accordance with Sect. 160. The finished sheet is to show 
all lines, letters, and figures, given in the copy. 

219. Sheet No. 27, Plate No. 53. — Before beginning this 
sheet the student should read Chapter VIII. on color work. 
The exercise is a first exercise for the brush, and is to be exe- 
cuted on a special paper. — different from that used for the pre- 
ceding sheets, in that the surface is not so highly calendered. A 
cold-pressed paper gives the best results. 

The paper should be neatly stretched on the board in accord- 
ance with Sect. 165; the ink used should be a "wash ink" pre- 
pared by rubbing stick ink in a saucer containing a small quantity 
of water. 

Directions for Drawing. — Lay out the sheet, according to 
the dimensions, in light pencil, being careful to draw only the 
lines necessary to block out the rectangles; do not draw lines 
within these spaces necessitating an erasure, thus bruising the 
surface, as this would show through the wash. Begin with 1 
and wash in the top row of rectangles; it will be noticed that the 
shade increases in depth; this is accomplished by, after each 



MECHANICAL EXECUTION OF DRAWINGS. 



211 



PLATE No. 48. 



z 
> 

m 



> 
H 
m 




THE CYCLOID 




o 

no 

Q) 
m 

> 

z 
o 



c 
z 
o 
> 

m 



o 

c 

< 

m 



*t» 






THE EPICYCLOID AND HYPOCYCLOID 

Y 



CO 

m 
m 

H 



to 
to 




THE INVOLUTE 






212 



MECHANICAL DRAWING. 



PLATE No. 49. 



Q 

H 5 

j- i 



C5 


JQ 
09 
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c 
at 


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LU 


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5 i 



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LU 

t 
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CD 


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03 






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ed 

jC 


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MECHANICAL EXECUTION OF DRAWINGS. 



213 



PLATE No. 50. 



CO 

Q 

O 

X 

UJ 



LU 



o 

< 

UJ 

CD 



en 



co 

>- 

CO 



LU 

tr 

LU 

u. 

u. 



CO 

C5 



0) 




♦ / 


3 









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OS 




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LU 








214 



MECHANICAL DRAWING. 



PLATE No. 51. 




MECHANICAL EXECUTION OF DRAWINGS. 



215 



PLATE No. 52. 




2i6 MECHANICAL DRAWING. 

wash, rubbing the stick of ink in the saucer; the tint should 
be inspected by sample on scrap-paper before applying. 

The shaded row is washed in in accordance with one of the 
methods for shading given in Sect. 168. It should be noted 
that J-A and j-B are alike and are the light washes of the row, 
that 8-^4 and S-B are alike and are a shade deeper than j-A 
and 7-5, and that g-A and g-B are alike and are the heavy shade 
of the row. 

The tinted row is washed in by first laying a flat wash over the 
entire rectangle, and when dry applying the shade as above. 

In the flat wash (top row) let the paper be first washed with 
clear water for one or two spaces that the student may note the 
effect ; the remainder of the sheet may be washed in directly. 

In executing the sheet, exercise great care in preserving the 
outline of the rectangles; should the color run outside, the edges 
may be straightened with a knife-point and eraser, a procedure, 
however, which does not add. to the beauty of the sheet and is 
to be avoided if possible. 

In inking, ink only the border-line of the sheet — not the borders 
of the rectangles — omit all dimensions, and finish the sheet by 
lettering the title and name only. When finished, cut the paper 
from the board with a \ ,r margin outside of the border-line on 
all sides. 

Place the sheet number — Sheet No. 27 — in the upper right- 
hand corner. 

220. Sheet No. 28, Plate No. 54. — This sheet is a wash draw- 
ing of plane surfaces which are parallel with, and inclined to, 
the plane of projection, and of concave and convex single-curved 
surfaces. 

To wash Fig. 1, begin on the left with the proper tint and 
draw it out to the right, washing entirely across the rectangle — 
do not attempt to define the center edge; when dry, begin at 
the center with the proper tint and draw it out to the right. For 
2, flat wash the parallel face and when dry shade the inclined 
sides as shown. For 3, lay on a light wash first, then treat each 
face in order according to the degree of shade. For 4, beginning 



MECHANICAL EXECUTION OF DRAWINGS. 



217 



PLATE No. 53. 




2i8 MbCHANICAL DRAWING. 

at the left, draw out the tint to the right and entirely across the rect- 
angle; when dry, begin at the right side and draw the tint to 
the left. For 5, flat wash the flat surfaces first, then shade as in 4. 

The next row, representing end views of the figures in the 
top row, are all flat washes. For 6, flat wash the circular draw- 
ing, also the rectangular section, first cross-hatching it with the 
ruling-pen and the wash ink. The shading of this figure may 
be done according to the fourth method of Sect. 168. Fig. 7 
is a flat wash of three tints. For Fig. 8, the circular drawing is a 
flat wash of two tints and the rectangular drawing a wash similar 
to the rectangular drawing of 6. 

Directions for Drawing. — Lay out the sheet, according to 
the dimensions, in light pencil; wash all flat surfaces first, then 
shade as directed above. In inking, ink the border only, and 
finish the sheet by lettering the title and name. 

Place the sheet number in the upper right-hand corner. 

221. Sheet No. 29, Plata No. 55. — This sheet illustrates 
certain well-known mechanical details, washed in as for cata- 
logue illustration, and introduces the application of Chinese- 
white for bringing out the lines. Fig. 1 represents a coil sping, 
2 a section of a cylinder disclosing a piston, 3 a portion of a 
square- threaded bolt, and 4 a hexagonal-headed bolt and nut — 
5 and 6 are end views. 

To shade the spring, cross-hatch the sections with the ruling- 
pen, using wash ink, then flat wash them; shade the front of 
the spring first, then the parts showing at the rear. To shade, 
wash in one curvature at a time; i.e., consider the top wire ex- 
tending across the front of the spring: beginning at the top, lay 
on a stripe of the tint all the way across, then draw it down at 
once ; when the surface is dry, begin at the bottom line and draw 
up at once; again allow the surface to dry, then beginning at the 
left hand lay on the wash and draw it to the right at once; next, 
shade the right end in a similar manner. 

The cylinder is shaded in a like manner, one curvature at a time. 
The section is cross-hatched, free-hand, with the tip of the brush- 
then flat-washed. 



MECHANICAL EXECUTION OF DRAWINGS. 



219 



PLATE No. 54. 




«0 



« 



fQ 




.cu 




lof® 







_i^_ 









91 











£V* 



— ,_<z. ■ -** 





.10 



9i 



-t 



V 






220 MECHANICAL DRAWING. 

The thread is also shaded one feature at a time. 

To shade the bolt and nut wash in all the flat surfaces, then 
shade as above. 

The white lines are ruled in with the ruling- pen and Chinese- 
white ink; this is done the last thing. 

Directions for Drawing. — Lay out the figures according to 
the dimensions, wash in as directed, and finish the sheet by letter- 
ing as shown. All dimensions are to be omitted. 

Place the sheet number in the upper right-hand corner. 

222. Sheet No. 30, Plate No. 56. — This sheet is a first exer- 
cise in stippling — shading with dots. The plate shows a plan 
and elevation of a hexagonal prism, a hexagonal pyramid, a 
cone, and a cylinder. The figures are first drawn in outline on 
a duplicate sheet; that is, the figures are laid out in the same 
arrangement relative to one another and to the border-line as they 
will appear on the stippled sheet, and are then cut out as follows : 

With a knife-point cut out the plan of the prism, cone, and 
cylinde: (5, 7, and 8). The first and last are flat surfaces and 
are stippled uniformly by placing the " stencil" on the sheet, 
border to border, and the dots thrown through the openings as 
directed in Sect. 170. To shade the plan of the cone (7), mat 
out, with strips of paper, all of the exposed surface except a 
small sector in the part to be darkest; stipple this about as for 
the flat surfaces, drawing the shade at the radii; now increase 
the area of the sector, then stipple the exposed surface lightly 
again — this will cause the first shaded portion to grow darker. 
Continue increasing the size of the sector in this manner until 
the entire circle is exposed, when the view will have been shaded. 

For the plan of the pyramid (6), cut through the stencil on 
the lines representing the edges and part way through on the 
base-lines; with the stencil in position, fold back the lower right- 
hand triangle and stipple the exposed surface rather dark; now 
fold back the bottom triangle — the first remains open — and shade 
the exposed area; next fold back the upper right-hand triangle 
and shade the exposed surface; proceed in this manner, taking 
the faces in the order of the degree of shade and shade the 



MECHANICAL EXECUTION OF DRAWINGS. 



221 



PLATE No. 55. 







W) 



-l«* 



■T 



11 » 



kvH 






222 MECHANICAL DRAWING. 

entire exposed area each time, thus causing the faces to grow 
aarker in the order of exposure. 

To shade the top row, i, 2, 3, and 4, cut out the side faces of 
the prism and of the pyramid, and the outlines of the cone and 
cylinder; place the stencil in position and shade the exposed 
surfaces according to the copy, care being taken to protect each 
surface after stippling; these shaded, cut out the front face of 
1 and 2 and stipple the exposed areas. 

Directions for Drawing. — In stippling, it is important that 
the stencil be protected, that is, when stippling an area, mat out 
the surface of the stencil immediately about the opening with 
scrap-paper, thus keeping the moisture off the stencil, which if 
allowed on would cause it to blister. It is also important that 
the stencil have good contact with the paper to produce clean- 
cut lines ; good results are obtained by laying small weights about 
the edges of the opening. 

In inking, ink the border-line only, omit all dimensions, and 
finish the sheet by lettering it as shown. 

Place the sheet number in the upper right-hand corner. 

223. Sheet No. 31, Plate No. 57. — Here is depicted for "show" 
purposes a form of insulator (1, 2, and 3) and an ornamental 
cap (4, 5, and 6). The figures are first drawn on the stencil- 
paper, then the sheet executed in the following order: 

Cut out 1, the interior of 2, the darkest circle of 3, all of 4, the 
interior of 5, and the center of 6; place the stencil on the sheet, 
border to border, weight the 1" center of 1 and 3 in position, and 
shade the exposed areas according to the copy. Next cut out 
the section of 2 and 5, the second circle of 3, and all of 6, then 
shade. Now cut out the ends of 2, all of 3, and the double curved 
part of 5; mat out with scrap-paper the exposed parts already 
stippled, then shade; lastly, cut out the groove of 3 and the 
single curved surface of 5, mat out exposed parts, and shade 
according to the copy. 

Directions for Drawing. — Ink the border-line only, omit all 
dimensions, and finish the sheet by lettering it as shown, 

Place the sheet number in the upper right-hand coiner. 



MECHANICAL EXECUTION OF DRAWINGS. 



223 



PLATE No. 56. 




224 



MECHANICAL DRAWING. 



PLATE No. 57. 




MECHANICAL EXECUTION OF DRAWINGS. 



225 



224. Sheets Nos. 32 to 36, Inclusive. — These are to be pen-and- 
ink scale drawings of the "working sketches " of the work in sketch- 
ing, constituting what will be termed "shop drawings " — draw- 
ings for shop purposes. These drawings are to be prepared in 
pencil on paper, and then traced in ink on tracing-cloth, and 
later reproduced in blue-print. 

Great care must be exercised in the preparation of these 
drawings to make them clear and complete in every detail, giving 
all necessary dimensions, notes, etc. 

225. Tables. — To work most efficiently a draughtsman 
should surround himself with tabulated statements of much-used 
information; if he be a designer, he should have tables of the 
diameter, circumference, and area of circles, the weight per cubic 
foot of the various metals, dimensions of standard parts, etc. 
The student in elementary mechanical drawing, while not needing 
a complement of such information, often has occasion to know 
the dimensions of the nut and number of threads per inch for 
a bolt of certain diameter, the size of tap-drill, etc., the size of 
steam- and gas-pipe, with the corresponding threading, informa- 
tion for drawing gear- teeth, etc. The following tables are ap- 
pended for reference in such cases : 

Steam- and Gas-pipe. 



Normal 
Size. 


Actual 


Actual 


Number of 


Inside 


Outside 


Threads 


Diameter. 


Diameter. 


per Inch. 


1 

8 


.27 


.40 


27 


1 

4 


.36 


•54 


18 


f 


.49 


.67 


18 


J 


.62 


.84 


14 


f 


.82 


1.05 


14 


I 


I.05 


I- 31 


II* 


ii 


I.38 


1.66 


II* 


i* 


1. 61 


1.90 


Hi 


2 


2.07 


2-37 


II* 


a* 


2.47 


2.87 


8 


3, 


3-<>7 


3-5° 


8 


3* 


3-55 


4 


8 


4 


4-03 


4-5 


8 


4* 


4-5i 


5 


8 


5 


5-°4 


5-56 


8 


6 


6.06 


6.62 


8 


1 


'aper of threads f " per i 


9 


. 




1 



226 



MECHANICAL DRAWING. 



Bolts and Nuts. 



Diameter 
of Screw. 


Threads 
per Inch. 


Diameter 

at Root of 

Thread. 


Distance 

between 

Flats, 

Hexagonal 

or Square. 


Diameter 

Across 

Corners, 

Hexagonal. 


Diagonal of 
Square. 


Tap-drill. 


i 


20 


.185 


§ 


37 /k 


% 


% 


% 


18 


.240 


19 /32 


% 


% 


\ 


f 


16 


.294 


% 


5 V64 


3 V32 


%, 


% 


14 


•344 


2 %2 


5 %4 


1^6 


2 %4 


\ 


13 


.400 


7 


I 


li 


13 /32 


% 


12 


•454 


% 


li 


1^6 


15 /32 


I 


II 


•5o7 


If 


I%2 


li 


17 /32 


1 


IO 


.620 


li 


1^ 


If 


f 


1 


9 


.731 


lJi6 


i 2 y 32 


2V32 


t 


I 


8 


•837 


If 


if 


2^6 


2 %2 


li 


7 


.940 


1% 


2%2 


2i 


3 y 32 


ll 


7 


1.065 


2 


2% 


2 27 / 3 2 


I%2 


if 


6 


1. 160 


2% 


2 17 /32 


3%2 


1% 


li 


6 


1.284 


2| 


O 3 - 
2 4 


38 


I%2 


If 


5* 


1.389 


2% 


2 3 y 3 2 


5 1 

3s 


I 13 /&2 


If 


5 


1.490 


2| 


3% 


3 2 %2 


ll 


2 


4* 


1. 712 


3* 


3l 


4% 


if 


2* 


4* 


1.962 


3| 


A%. 


4 3 Vs2 


I 3 V32 


2^ 


4 


2.I7S 


3* 


4i 


Si 


2% 


2| 


4 


2.425 


4* 


4 2 %2 


6 


2j^ 


3 


3l 


2.628 


4f 


5-1 


6% 


2f 


3i 


3* 


2.878 


5 


5% 


7 t 


2 2 %2 


3§ 


3* 


3.100 


St 


6Ve* 


?L 


3V32 


3f 


3 


3-317 


5f 


6 2 %2 


8^6 


3 1 V32 


4 


1 3 


3-566 


6 


7%2 


s% 


3 19 /32 



Angle of thread=6o°. Thickness of nut= diameter of bolt. 
head= one-half distance between flats. 



Thickness of 



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Treatise on Concrete, Plain and Reinforced 8vo, 

Thurston's Materials of Engineering. In Three Parts 8vo, 

Part I. Non-metallic Materials of Engineering and Metallurgy. . . .8vo, 

Part II. Iron and Steel 8vo, 

Part III. A Treatise on Brasses, Bronzes, and Other Alloys and their 

Constituents 8vo, 

Tillson's Street Pavements and Paving Materials 8vo, 

Turneaure and Maurer's Principles of Reinforced Concrete Construction. 

Second Edition, Revised and Enlarged 8vo, 

Waterbury's Cement Laboratory Manual 12mo, 

* Laboratory Manual for Testing Materials of Construction 12mo, 

Wood's (De V.) Treatise on the Resistance of Materials, and an Appendix on 

the Preservation of Timber 8vo, 2 00 

Wood's (M. P.) Rustless Coatings: Corrosion and Electrolysis of Iron and 

Steel 8vo, 4 00 



RAILWAY ENGINEERING. 

Andrews's Handbook for Street Railway Engineers 3X5 inches, mor. 1 25 

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Brooks's Handbook of Street Railroad Location 16mo, mor. 1 50 

* Burt's Railway Station Service 12mo, 2 00 

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Fisher's Table of Cubic Yards Cardboard, 25 

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Hudson's Tables for Calculating the Cubic Contents ot Excavations and Em- 
bankments 8vo, $1 00 

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* " " " Abridged Ed 8vo, 

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Elements of Drawing. (In Press.) 

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Emch's Introduction to Projective Geometry and its Application 8vo, 

Hill's Text-book on Shades and Shadows, and Perspective 8vo, 

Jamison's Advanced Mechanical Drawing 8vo, 

Elements of Mechanical Drawing 8vo, 

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Shadow 12mo, 

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